Does anyone else remember playing Electronic Stratego? The version where the identity of each piece was encoded on the bottom with a series of bumps? It was an even more incomplete information game: attacking a piece would only let you know if the piece was higher, lower, or even, instead of revealing the piece's identity. I played it so much as a kid that I can't even think of Stratego without hearing that electronic bomb sound in my head. I feel it is actually a better game than the original.

https://en.wikipedia.org/wiki/Stratego#Electronic_Stratego

Would be fun to build this using cryptography (probably some kind of MPC).

That is the rules we used for playing stratego. Attacker reveales his piece number and the defender declared who won, or obviously if both died they were even.