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 Stock

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.