According to this page on English:
Do not capitalize games or dances.
Example: checkers, hop scotch, tango
If a proper adjective appears with a game or dance, capitalize the proper adjective but not the name of the game or dance.
Example: Mexican hat dance, Chinese checkers
So you are correct to refer to it as simply chess because it is the name of a game. However, if you were writing about a game such as Sims, you would capitalize the title because it is a proper noun. Daily Writing Tips has a full post on this, saying:
Those of strategy games such as chess and checkers are lowercased, too (but note “Chinese checkers”), as are names of tile games such as dominoes. Traditional children’s games like tag and hopscotch, and those with more complex names, such as capture the flag, hide-and-seek, and king of the castle, need no special emphasis, either.
Brand names of trademarked games like Monopoly, Scrabble, and Chutes and Ladders are capitalized, but note that it is not necessarily to use registration symbols with them. (You will, of course, note the r in a circle adjacent to the brand name on the game itself and in printed and online literature published by the company, as well as in written materials of any company affiliated or in partnership with the trademark holder, but no other publication is required to include such symbols.)
When chess is capitalized, it is usually part of a title--for example the World Chess Champion.