For the Analysis board they are using Stockfish.js 8. I assume they are using the same for the play vs computer with hard limits on how many ply they allow the engine to go, likely with some other tweaks to hobble it more on the lower levels.
Not sure if they use the same for the bots in Live though.
For the play vs computer and analysis, the code runs on the client, so hardware does play into it. For the Live bots, they are playing on the server hardware.
I'm curious about which version of Stockfish Chess.com is currently using and a few related things. I noticed that Level 10 computer is rated ELO 2600. Would that be Stockfish 8 or is it more complicated than that? Also, does anyone know how many moves deep the chess engine on Chess.com thinks, or is it not simply brute forcing but also doing some pruning to only certain lines? Given that Stockfish is open source, does Chess.com pretty much always use the latest version? Does the strength of the chess engine vary significantly depending on the device? E.g. laptop vs cell phone? Any thoughts would be much appreciated!