The wild west had many “shoot-outs” (or “shootouts”). From about the 1960s, athletic competitions (mostly football games) began to be called “shootouts.”  The annual football battle between the University of Texas Longhorns and the Oklahoma University Sooners was called the “Red River Shootout,” trademarked from 1987. (It is now called the “Red River Rivalry.”)
 
The national championship football game between the #1-ranked University of Texas and #2-ranked Arkansas in 1969 (Texas won a thriller) was called a “shootout” by many, but it was not the first such use of the term.
 
 
(Oxford English Dictionary)
shoot-out, n.
Also shootout.
 
1.a. A sustained exchange of shooting, a gun-fight.
1953 N.Y. Times 5 July VII. 13/2 The justly famous shoot-out between the Earps and the Clantons in the O-K Corral.
1.b. fig. An intense and decisive contest.
1975 Business Week 27 Oct. 94 F He would like congress to fund a ‘shoot-out’ contest between two prototype platforms.
   
This Dog’ll Really Hunt:
An Entertaining and Informative Texas Dictionary
by Wallace O. Chariton
Plano, TX: Republic of Texas Press
1999
Pg. 60:
Confrontation:
(...)
3. a shoot-out
[In 1969, when No. 1 Texas played No. 2 Arkansas for the National Championship of collegiate football, Longhorn coach Darrell Royal referred to the game as a shootout. Since then major sports confrontations have frequently been referred to as shootouts.} 
   
23 March 1966, Dallas Morning News, section B, pg. 1:
Little things, really, but still disturbing when you consider that some other team won the title in a fair-and-square shoot-out.
   
5 November 1967, Dallas Morning News, section B., Pg. 1 headline:
Texas, Aggies Win Wild Shootouts
     
1 December 1967, Dallas Morning News, section A, pg. 1:
THE TEXAS Power & Light Co. executariat was a collection of mixed emotions during the recent shoot-out for the Southwest Conference football championship.
 
20 September 1968, Dallas Morning News, “Shootout at Austin” by Roy Edwards, section B, pg. 2:
SEPTEMBER IS a bit early for shootdowns and shootouts and crucial games in college football, especially for teams that haven’t teed it up yet.
 
27 September 1968, Dallas Morning News, section B, pg. 1:
SWC Shootout Starts
‘Horns, Tech in Conference Opener
 
3 November 1968, Dallas Morning News, section B, pg. 1:
Longhorns Take SWC Shootout, 38-7
 
4 December 1969, Dallas Morning News, section B. pg. 3:
Whoever they’re playing Saturday in the nationally-televised No.1-vs.-No. 2 shootout on the Razorback’s Astro-turf, the Razorbacks will be coming at Worster and the Longhorns with a unit that leads the nation in defense against scoring, and, as Texas Tech coach J. T. King put it, majors in big plays.
   
5 December 1969, Dallas Morning News, section B, pg. 3:
It should be. then, a milestone game, a monumental struggle, an epic shootout.
 
(Trademark)
Word Mark RED RIVER SHOOTOUT
Goods and Services IC 041. US 100 101 107. G & S: organizing and conducting competitive sports events, namely golf tournaments. FIRST USE: 19871001. FIRST USE IN COMMERCE: 19871001
Mark Drawing Code (1) TYPED DRAWING
Serial Number 74608421
Filing Date December 8, 1994
Current Filing Basis 1A
Original Filing Basis 1A
Published for Opposition December 12, 1995
Registration Number 1983543
Registration Date July 2, 1996
Owner (REGISTRANT) Red River Classic Association, Inc. NOT-FOR-PROFIT CORPORATION TEXAS 3300 Lincoln Plaza 500 N. Akard St. Dallas TEXAS 75201
Attorney of Record MARTIN KORN
Disclaimer NO CLAIM IS MADE TO THE EXCLUSIVE RIGHT TO USE “SHOOTOUT” APART FROM THE MARK AS SHOWN
Type of Mark SERVICE MARK
Register PRINCIPAL
Affidavit Text SECT 15. SECT 8 (6-YR). SECTION 8(10-YR) 20050913.
Renewal 1ST RENEWAL 20050913
Live/Dead Indicator LIVE
 
(Trademark)
Word Mark OKLAHOMA-TEXAS SHOOTOUT
Goods and Services (CANCELLED) IC 041. US 101. G & S: conducting entertainment exhibitions in the nature of rodeos. FIRST USE: 19910207. FIRST USE IN COMMERCE: 19910207
Mark Drawing Code (1) TYPED DRAWING
Serial Number 74277354
Filing Date May 19, 1992
Current Filing Basis 1A
Original Filing Basis 1A
Published for Opposition October 27, 1992
Registration Number 1747516
Registration Date January 19, 1993
Owner (REGISTRANT) COWTOWN BOOT CO., INC. CORPORATION TEXAS 11401 Gateway West P. O. Box 26428 El Paso TEXAS 79926
Attorney of Record Charles A. Codding
Type of Mark SERVICE MARK
Register PRINCIPAL
Live/Dead Indicator DEAD
Cancellation Date July 26, 1999
 
(Trademark)
Word Mark RED RIVER RIVALRY
Goods and Services IC 025. US 022 039. G & S: Clothing, namely, caps, jackets, coats, shirts, warm-up jackets, warm-up pants, t-shirts, sweaters, raincoats, ponchos, sweatshirts, sweatpants, running and athletic shorts, tank tops, wind suits, and jerseys. FIRST USE: 20050800. FIRST USE IN COMMERCE: 20050800
IC 041. US 100 101 107. G & S: Entertainment services, namely, organizing, promoting, and staging college sports games and events. FIRST USE: 20050800. FIRST USE IN COMMERCE: 20050800
Standard Characters Claimed
Mark Drawing Code (4) STANDARD CHARACTER MARK
Serial Number 77131853
Filing Date March 15, 2007
Current Filing Basis 1A
Original Filing Basis 1A
Owner (APPLICANT) The Board of Regents of The University of Texas System STATE AGENCY TEXAS 201 West 7th Street Austin TEXAS 78701
(APPLICANT) The Board of Regents of The University of Oklahoma STATE UNIVERSITY OKLAHOMA Suite 213, 660 Parrington Oval Norman OKLAHOMA 73019
Attorney of Record William H. Brewster
Type of Mark TRADEMARK. SERVICE MARK
Register PRINCIPAL
Live/Dead Indicator LIVE