They have a huge database of most common moves + chess engine moves they cross reference to, then using math they see if your time to move + accuracy of moves is close to a chess engine, especially if it's not the opening (since being accurate for the first 4-12 moves is trivial). If you play too fast and with too much accuracy relative to your ELO you get banned pretty quick.

It's "Elo", not "ELO".

Afaik they analyze the deviation (in centipawns) of each played move to the optimal move calculated by popular chess engines (like Stockfish, Houdini, Komodo, etc); and aggregate in a sort of weighted Brier score.

If a player is constantly making optimal moves, they're likely cheating (they can analyze top level professional matches for upper skill benchmarks). There is some lower weighting for opening moves (which is where the database part comes in just knowing when a game moves from theoretical 'book' openings into original territory).

Each of the sites have different implementations of this: chess24 for example even partially gives your accuracy of book moves and then differentiates between Blunder / Mistake / Good / Excellent / Best move based on the deviation from optimal; but it doesn't show you how it's aggregated into a single value.

re: move speed - it's also often that low rated players using engines take too long on trivial moves - many chess engines will take a set amount of time to look for the best move, even if there's something completely obvious on the board like capturing a queen that you've spent the last three moves trapping.