The short story "Duel on Syrtis" by Poul Anderson,
written in 1951, is one of 8 short stories from his book
"Strangers from Earth". It is in my opinion, very interesting.
It had me quite interested and emotionally involved.
The alien native Martians were a protected species,
but rich Earth man Riordan really, really wanted one for
his trophy case and was quite sure he had figured out
how to hunt the toughest ever prey down and mount it.
from
http://www.goodreads.com/book/show/6458015-earthman-beware-and-others
is the narrative:
"DUEL ON SYRTIS
Although it was illegal to hunt Martians for sport, when one had a
enough money the laws could be circumvented. Riordan had the money now
he wanted the skin of Martian to hang on the wall of his trophy room. Of
course the Martian has other ideas."
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Seems like a real common & old topic,
where all have we seen it before this?
https://en.wikipedia.org/wiki/The_Most_Dangerous_Game (1924)
"The story has been adapted numerous times, but most notably
for the 1932 RKO Pictures film The Most Dangerous Game, starring
Joel McCrea and Leslie Banks, and for a 1943 episode of the CBS
Radio series Suspense, starring Orson Welles."
'"The Most Dangerous Game" is a popular read within middle and high
school curriculums due to the strength of the themes within the story.'
Below are cut & pastes from that wiki --
A Game of Death (1945)
Run for the Sun, starring Richard Widmark, 1956
In 1961, the film Bloodlust!
Brian Trenchard-Smith's Turkey Shoot and its remake Turkey Shoot (2014)
Jean-Claude Van Damme thriller Hard Target (1993), was loosely based on
the same story.
In Surviving the Game (1994)-- the film stars Rutger Hauer, Ice-T, and
Charles S. Dutton.
In The Eliminator (2004),
The Pest (1997) is a comedic parody of the story,
Get Smart episode, "Island of the Darned"
This trope was used in the season 3 (1968), episode 22 of I Spy, "The
Name of the Game".
In the pilot episode of Fantasy Island, a big-game hunter comes to the
island to be hunted by a man, an interesting twist on the usual version
in which the hunted participates against his will.
In the Gilligan's Island episode "The Hunter", big-game hunter Jonathan
Kincaid (Rory Calhoun) turned his sights on Gilligan when he realized
there were no wild animals on the island.
In the series finale of Bonanza, entitled "The Hunter", a deranged
killer, Corporal Bill Tanner (Tom Skerritt), who was formerly a tracker
for the United States Army, hunts Little Joe (Michael Landon).
The Canadian series Relic Hunter had an episode called "Run Sydney Run"
that was very closely based on The Most Dangerous Game, with Peter
Stebbings acting as General Tsarlov.[citation needed]
also
https://en.wikipedia.org/wiki/Category:Death_games_in_fiction
It sure seems on the edge of my memory that there was
a Star Trek episode on this. ??