I think this short story is from the 1970's or 1980's.
The story opens when rescuers find a human that was stranded alone on a spaceship for many years. How he got stranded alone on a spaceship is not mentioned as far as I can remember. During that time, he plays many kinds of games against the ship's computer over and over to stave off boredom. Over the years, he becomes an expert at many strategy games.
His human rescuers bring him to a planet that's nearly covered by ocean except for a few islands. The oceans have enormous (building-sized) sea creatures with long tentacles. The short story does not provide much information about the names, culture, history, or personalities of the sea creatures. By the time of the man's rescue, humans had been in contact with the aliens for some years.
These creatures teach humans a complex game involving many thousands of pieces all over a sphere-shaped game board. The man learns the game and quickly becomes very good at it to the point where he develops novel tactics to defeat the other human players.
The story ends when ...
the sea creatures invade Earth's oceans and use the tactics they learned from the game expert to take over the Earth.