Back in the mid to late 80s there were drastically different pricing for VHS movie rentals. New releases could cost $5-$8 for a single 24 hour rental. Some rental stores had a middle tier price/time structure as well....then there was the garbage tier rentals of 99 cents for anywhere from 24 hours to a week.
Gymkata was one of those movies that would regularly be found on the 99 cent garbage tier movies. When you're scraping together coins for a to afford a 99 cent rental for Friday night, you want to get one of the best garbage tier movies you can.
Gymkata was always a regular at the top of the list of favorite garbage tier rentals! We rented it many times!
Oh no, the game doesn't have anything to do with gymnastics per se. It's just that the Main character is played by an gymnast and they apparently wanted to make an action movie around that gimmick.