Ah.
Yes.
"Entertainment."
I have low expectations; to invent chess, one must first have some concepts that require thoughts wayyyyyyy the fuck beyond the game itself.
I mean, games that only involve diagonal movements, or perpendicular movements; games with one type of piece, games with multiple movement schema; these all can lead you to chess, and chess is fairly simple to play, but to invent chess?
If you have chess, you have at least 200 other "board games" for possible "Entertainment."
Maybe it's silly, but you don't magically have chess without having a bunch of other games already existing.
And dont get me started on the invention of ball games!
In the Middle Ages, Gambol, Fusball, Football, Tenez, Futbol/Soccer, and Tennis alone have insane backstories involving monasteries, dead spouses, castles, murdered players, and even the Pope getting involved!
So... nah; they don't "only have Chess" any more than Americans dont have soccer/futbol (which we all learned this week, it seems).