If you enjoyed this, you might like Mind Chess, which can be played without a board and pieces [1]:
Consider Mind Chess. Two players face each other. One says "Check." The other says "Check." The first says "Check." This continues until one of them says, instead, "Checkmate." That player wins -- superficially. In fact, the challenge is to put off checkmate for as long as possible, while still winning. This may be better stated: you truly win Mind Chess if you call "Checkmate" just before your opponent was about to.
And if you like Mind Chess, you might enjoy Mornington Crescent, which has a similar flavor to it! [1]
Speaking of games without pieces, it's hard to develop one for only 2 players, but I've tried: https://news.ycombinator.com/item?id=43110448 (yes that is my alt account, sorry but I forgot my password)
Sounds like a dating game. "Delay texting her back or expressing your feelings as long as possible, until just the moment before she will give up on you"
Wait, how is the "put off checkmate" objective scored? Turns before checkmate? Or what?
Is it just a joke?
Which reminds me that I just lost the game.
I also lost the game not too long ago, but before that, I think I didn't actually lose it for a decade of more? And losing it wasn't even because it was mentioned anywhere, I genuinely just thought of it by myself, after forgetting about it for so long.
So my sincerest apologies if my comment just made any readers lose their long streak in the game.