I've been giving this exact idea some thought recently (mostly since the 7DRL jam, which alas, I couldn't do). I'm still picking away at the design--currently trying to satisfy myself with how I'd want to implement it, bleh.
I came up a few; mechanically speaking, if a game features these in some way, then it smells Chessy.*
- There are two sides mired in conflict (black/white).
- The pieces involved have characteristic movement and action
- Pieces are valued differently.
- Each unit on the board has coordinates to it (grid- or map-based)--whether it has a chequered pattern or not is just a slider that moves between more and less Chess-like. Pattern could be something else (changes the effect of certain rules).
*Footnote: Oh, I went there. I made that pun.
Edit: Oh, and might I recommend people look at Chess variants for inspiration? Please do. It's fascinating what's come before!