Min-max + alpha-beta pruning is the backbone of the chess engines. I think 2KiB or even 1KiB might be enough (I guess the last one would be a very challenging squeeze). But what separates the best engines from average ones, is the heuristics. Heuristics is the most complicated one, and I doubt it's possible to fit it into a single-digit kilobyte memory (even 2-digit). For heuristics, engines like Stockfish also use neural networks, in addition to hand crafted algorithms. Also huge tables are used for endgames, etc.