“Chinese handball” is similar to “American handball.” It is called “Chinese” not because it comes from China or was popular in Chinatown or was played by Chinese players, but probably simply because it’s a different game and “Chinese” was the slang of the period. (See the July 1972 citation below.) Another name for the same game is “Ace-King-Queen.” In Chinese handball, the ball bounces on the pavement before it hits against a wall.
 
Chinese handball was usually played with a small pink ball called a spaldeen. The game was popular in New York City since at least the 1930s.
   
   
Wikipedia: Chinese handball
Chinese handball (also known as Ace-King-Queen, King(s), and Slugs), is a form of American handball popular on the streets of New York City and Bridgewater, NJ during the 1960s and ‘70s, and is still played today. In the Philadelphia region it is known as Chink, with almost all of the same rules.
 
Game play
Similar to one-wall handball with an opposite twist (“Chinese”), instead of hitting a ball against the wall to opposing players after the first floor bounce as in a normal handball scenario, would hit the ball (normally a spaldeen or kick pinkie) to the ground first toward the direction of the wall. The ball would then bounce off the wall and to the intended player. That player would either return the ball (the same way) back to the server or another player down the line.
 
A player may continue to hit the ball in his own box as long as he desires. This leads to set up shots where smaller and smaller bounces produce a difficult ‘baby’ shot that is sent to the next box. Alternately, low, long strokes develop a hard to return power shot to another box, or ‘Baltimore Chops’ a high bouncing shot. Some local rules may vary such as an ‘Ace’ knocked out of the lead box does not get a letter.
 
If a ball takes an erratic bounce due to a crack, or obstacle, on the court a player may call ‘Hindoo’ (from ‘hinder’ in Handball) and the ball is replayed with no letter assigned.
 
Any player failing to eventually return a ball from his box into another box receives a letter (‘K’, then ‘I’, then ‘N’, when he has the previous letter) and goes to the end of the line. At each change of position there is normally a shout out of each player from the ‘Ace’ stating his letters. When a player has all the letters that spell ‘KINGS’ the game is over and the losing player must face the penalty known as ‘asses up’ which consists of the losing player bending over with his head against the wall and his buttocks up while each of the other players take turns having three throws of the ball from across the street at the loser’s buttocks, any hit on the buttocks (legs and back do not count as a hit) gives everyone another turn of three throws. Not a game for the fainthearted.
 
The line consists of 2 to 20 players, with the first player being the “Ace”. The second player is the “King” and the third is the “Queen”. The final player in line is known as an “Ace Killer” because of his opportune position to take out the “Ace”.
 
Chinese Handball is a game that requires much strategy and reflexes.
 
Streetplay.com
Ace-King-Queen (Chinese handball)
This game is a hybrid between handball and boxball, and it can be played anywhere that a decent wall and sidewalk meet. Each player (anywhere from two to six) has a box that they defend. The player on the leftmost side (the “Ace”) serves by bouncing the ball on the ground first, where it then hits the wall and goes into the “box” (defined by cracks in the sidewalk) of the player on his right (the “King”). That player then hits it in the same manner against the wall and into the box of the next player (“Queen”), and so on down the line (each player in line gets the name of the descending card in the deck). When the last player receives the ball, he switches its direction, sending it back on its journey towards the Ace. As in handball, the ball can bounce only once, either arriving at or leaving the wall.
 
If a player misses the ball or hit its out of bounds, he gets a point and moves to the end of the line. Play to 11 points; the loser might be subjected to asses-up, the game’s most endearing feature. Needless to say, this is the part that everyone remembers.
 
One of the most distinguishing features of Ace-King-Queen is that you’re in control of your own box and can keep the ball in play by hitting it to yourself. A player might work the wall, refining the shot, hitting it against the wall again and again, until the bounce is perfectly positioned, whereby he can slam it over into his opponent’s box. “Waterfalls,” “skinny minnys,” and other terms that describe these tactics are important concepts in the lexicon of the game. Alternatively, sometimes Ace-King-Queen is played without boxes (probably the case in our picture on this page) and each player must go in order—or lose the point. Sidewalks typically have boxes, whereas pavement doesn’t.
 
So why do some people call it Chinese handball? Is it because it originated in China? Maybe in Chinatown, or other Asian neighborhoods? Is it Chinese because the rules are different from the standard game, and therefore the opposite of Western convention? It’s obvious that this term was coined long before our politically correct era! Who knows, but whether you call it Ace-King-Queen or Chinese handball, this is a major street sport.
 
(Dictionary of American Regional English)
Chinese handball n
A version of handball played outdoors.
1970 DARE (Qu. EE33…Outdoor games) Inf NY241, King-queen or Chinese handball—each player gets a cement block section of the sidewalk. First is king, then queen, jack, etc.
1981 Verbatim Letters NYC (as of 1930s), Chinese Handball was played against any convenient wall and was, in all respects the same game as conventional handball, except that the ball was required to bounce on the ground before it hit the wall.
 
20 July 1955, El Paso (TX) Herald-Post, “Kids of the 30s Seem to Have Had More Fun in Sports” by Charles Sutton, pg. 16, col. 1:
Back in Brooklyn, if we weren’t stopping traffic with a game of touch football, or crashing hedges in a game of tag, we were probably playing a fast game of handball on a tenement wall. Usually the wall was neatly decorated with a sign that read: No ballplaying allowed. For a change, we switched to Chinese handball, which meant sending the ball against the brick on a bounce.
 
15 June 1958, Charleston (WV) Gazette-Mail, magazine, pg. 28, col. 3:
NOT AS A CROCODILE, by Arthur Marx, Harper, $3.50.
(...)
“Of course, he was too young for golf—even for caddying—but I taught him baseball and touch football, and he taught me Kick-the-Can and Chinese handball.
 
Google Books
Growth Through Play
by Albert M. Farina
New York, NY: Prentice-Hall
1959
Pg. 229:
Diagram 8.16 CHINESE HANDBALL OR “KINGS” This game is usually played against a building by 3 to 6 players. Each player stands in a box bounded by the cracks ...
   
1 September 1963, New York (NY) Times, pg. BR3:
THE LORDLY HUDSON. Collected poems of Paul Goodman.
(...)
At least, I miss two of the pieces I liked best in “The Copernican Revolution,” a verse pamphlet Mr. Goodman published in 1947: “A Game of Chinese Handball” and “K.P.E. Bach.”
   
29 April 1968, New York (NY) Times, “Children Street Play Changes in City,” pg. 45:
Handball hangs on desperately s a street game. But it is mostly played on playground courts instead of against tenement, factory or garage walls. And even when it is played in the street it is now the milder form, known as “Chinese” handball, in which the player has to hit the ball so it bounces once before it reaches the wall. Some boys playing this game on East 91st Street, near Second Avenue,  did not even know it had a name.
 
27 July 1972, Dallas (TX) Morning News, “Sheinwold on Bridge” by Alfred Sheinwold, section AA, pg. 6:
When I was a boy the word “Chinese” was used to describe the reverse of the normal. In Chinese handball, we hit the ball at the ground instead of at the wall; in Chinese bridge we played the cards counterclockwise; Chinese checkers bore little resemblance to ordinary checkers and so on.
 
29 August 1972, New York (NY) Times, “Spaldeen Olympiad Is Proclaimed—and Anyone Can Play” by Michael T. Kaufman, pg. 35:
The events include stickball, stoopball, Chinese handball, boxball and Johnny on a Pony. All but the last are played with a pink rubber ball, known as a Spaldeen.
(...)
CHINESE HANDBALL. Played by five individuals who slap Spaldeen on pavement and against wall in front of five adjoining boxes. If player fails to hit ball slapped into his box after the first bounce, he gets a demerit and moves to the last box to the right. If he gets seven demerits, he’s out. This is called “Chinese” to distinguish it from “American,” in which the player slaps the ball directly to the wall instead of hitting it to the pavement and bouncing it to the wall. There is also “Chinese-American,” but who cares?
 
19 November 1980, New York (NY) Times, “Metropolitan Diary” by Glenn Collins, pg. C2:
THINGS I LEARNED THAT ARE NOW USELESS
1. Cutting (i.e., putting English on the spaldeen while playing Chinese handball).
 
Google Books
New York Street Games and Other Stories and Sketches
by Meyer Liben
New York, NY: Schocken Books
1984
Pg. 103:
I don’t know why the game is called Chinese handball. The name obviously has something to do with the required bounce, which distinguishes the game from what we sometimes called American Handball, but what the relation is between the bounce and China remains a mystery.
 
Google Books
Sporting with the Gods:
The Rhetoric of Play and Game in American Culture
by Michael Oriard
Cambridge University Press
1991
Pg. 454:
...the game of “Chinese handball” in Paul Goodman’s Making Do (1963), played by Irish, black, Jewish, and Spanish kids who share an hour of exuberance in the midst of the impersonal city;...
 
Google Books
Language in the Inner City:
Studies in the Black English Vernacular
by William Labov
Philadelphia, PA: University of Pennsylvania Press
1998
Pg. 340:
Your mother so low she c’play Chinese handball on a curve (curb) is a safe sound. Nobody is that low.