Well it stands to reason doesn't it? Gymnastics and martial arts are a match made in heaven. Let's make a film about it...
Gymkata is a very odd film and definitely in the "so bad it's good" drawer with plenty of unintentional humour. An actual Olympic gymnast Kurt Thomas was bought in as the star (and truth be told he is a non-actor but you will see a lot worse acting in these kinds of films by people who are supposed to be professionals). Our hero is sent into a tiny Central Asian country where the US wants to put a satellite monitoring station. The reason a gymnast martial artist and not a diplomat is sent in is because this little country gets foreign visitors to take part in an extreme endurance event chased by local warriors. A cute custom though as it results in most entrants deaths it can't be doing much for the tourism industry.
Win the event however and you are granted your wish, and hence a satellite base. Which is why the US sends in Kurt Thomas and not Casper Weinberger who I suspect is not that good at kung fu.
So that's what the film is about and it is all very silly. The Central Asian country is basically still in the Middle Ages and a very dangerous land full of grotesque stereotypes and freaks. The action is good though but the gymnastics part of the film is a bit contrived, remote villages just happening to have a pair of parallel bars...