List of games that Buddha would not play
en.wikipedia.org
en.wikipedia.org
I found it quite surprising that blindfold/mental variants of board games existed then, but thinking about it further there is no reason to be surprised about that I suppose. Many of the games discussed here seem more "modern" than I would have thought.
It is interesting that Chaturaji and Chaturanga are omitted, though I am inclined to believe that is because they didn't exist yet, rather than them being expressly permitted. That seems consistent with the timelines of each: [0] [1] So it would seem that all of the existing board games in India at the time were race games. [2]
[0] https://en.wikipedia.org/wiki/Chaturanga
Go is tricky to classify. It may have been designed or used to develop strategic war skills. Another view is sharing an economic market where trying to take too much will result in loss.
Nice loophole
These games exist nowhere but in ego consciousness.