The extent of my gaming would probably boil down to a good old round of "choke the chicken" if time allows.
Fun fact: lots of people who've been in exhaustion-inducing survival situations have mentioned that you have almost zero energy or interest in sex/self-service. Even on shows like Survivor where the cast is only just sort of half-surviving on their own, and where they're usually surrounded by attractive scantily-clad people of both sexes, they've mentioned there's almost no interest in it.
Unless the island you wind up on has tribal natives who take up worshipping you as a god and thus bring you all the food and fresh water you want and maintain your shelter for you, the effort you expend staying alive will probably discourage you from any extracurricular activities along those lines.