A “hat trick” in ice hockey is when a player scores three goals in one game. Gordie Howe (1928-2016) played professional hockey from 1946–1971 and then from 1973–1980; he was known for his scoring ability and his physical strength. A “Gordie Howe hat trick” is when a player has one goal, one assist and one fight in the same game.
 
“Gordie Howe hat trick” has been cited in print since at least 1989—just after Howe’s playing days (although he was signed for one game in 1997). Howe himself had only two “Gordie Howe hat tricks”—in 1953 and in 1954.
 
   
Wikipedia: Gordie Howe hat trick
In ice hockey, a Gordie Howe hat trick is a variation on the hat-trick, wherein a player scores a goal, records an assist, and gets in a fight all in one game. It is named after Gordie Howe, well known for his skill at both scoring and fighting.
 
The Gordie Howe hat trick is not an official statistic. Its conception is relatively recent; The Hockey News has statistics on it only since the 1996–97 NHL season.
 
17 December 1989, St. Paul (MN) Pioneer Press, “North Stars Snap Road Slump, 4-3,” pg. 1C:
“Basil got a `Gordie Howe hat trick,’” Dave Gagner said. “He scored a goal, got an assist on the winner and got into a fight. A hell of a fight!”
 
23 December 1991, St. Louis (MO) Post-Dispatch, “Shanahan Scores Points With Fists Against Islanders” by Dave Luecking, pg. 8C:
After the game, Shanahan called his performance a “Gordie Howe hat trick: A goal, an assist and a fight.”
 
22 April 1993, St. Albans (VT) Messenger, “Expansion teams make network debut” by John Nelson (AP), pg. 16, col. 4:
Bob Miller, for 20 years the voice of the Los Angeles Kings and Prime Ticker’s hockey play-by-play announcer, has his own peculiar vocabulary. OK, “biscuit” for puck and “twig” for stick are pretty easy to figure out, but what’s a “Gordie Howe Hat Trick?”
 
That, explains Miller, is when a player gets “a goal, an assist and into a fight all in the same game.”
   
Sports Illustrated
March 24, 1997
The Worst Job In Sports
WHILE SOME NHL ENFORCERS LIKE TO BRAWL, MANY MEMBERS OF THE FRATERNITY OF FIGHTERS FIND IT DANGEROUS AND DEMEANING, AN UGLY WAY TO EARN A HANDSOME LIVING
Michael Farber
(...)
Nilan and McSorley are the idols of every roughneck who dreams of attaining a Gordie Howe hat trick: a goal, an assist and a fight in the same game.
 
Google Books
The Best of Everything Hockey Book
By Shane Frederick
Mankato, MN: Capstone Press
2011
Pg. 26:
Any player who scores a goal, gets an assist, and gets in a fight achieves a “Gordie Howe hat trick.” Howe played professional hockey until 1980 at age 51.
 
Google Books
The Sports Hall of Fame Encyclopedia:
Baseball, Basketball, Football, Hockey, Soccer
By Dave Blevins
Lanham, MA: Scarecrow Press, Inc.
2012
Pg. 462:
On December 26, 1917, Harry Cameron became the first player to achieve what is now called the “Gordie Howe hat trick,” when a player scores a goal, gets an assist, and participates in a fight.