No. Computers don't play chess by "simply enumerating all possible boards". That would require ludicrously more compute power than we have, and, of course, it would also _solve_ chess, rather than just allowing the computers to play once it would (if it could ever be done) show that the game itself has a solution, a best way to play, like Tic-Tac-Toe.
Historically AI chess (e.g. "Deep Blue" or Stockfish) is played by machines using one heuristic to estimate how "good" positions are without truly knowing, not so dissimilar from how humans evaluate a chess position. and then another heuristic to try out moves to get to further positions. The machine considers possible plays and how they affect the heuristic "value" of the board, preferring those with more value. Human Chess AI authors design the two heuristics used, though they often aren't very good at actually playing chess because it's a different skill.
Google's AlphaZero AI plays chess differently again, it had no preconceptions of how to play Chess, instead it learned through self-play - it knows the rules of the game but began with no idea what's a good or bad move, it adapted its own heuristics based on how well they'd won or lost. It actually recapitulated most of human chess theory history over its incubation period of thousands of games, discovering ideas like the Sicilian Defence for itself, new attacks would at first see overwhelming success, and then, playing versions of itself that had seen these attacks, they'd be defended more effectively.
Alpha Zero plays a radically "more human" style of chess than most modern human Chess grandmasters, huge multi-move strategies in which pieces are sacrificed to take positional advantage. It looks like something humans were doing last century - except Alpha Zero does it much better than they ever did.