is the engine correct here?

It seems to me that if my opponent had made that pawn move instead of taking the knight, they'd just be offering me a free pawn, while the f pawn would still be pinned to the king and then they could still take the knight. But maybe that's why I'm not a chess engine (not yet).

In this position, black is down a whole rook. There is no magical tactical trick in the position.

It does not matter what they play, black is completely  lost.

According to Stockfish, d5 is not in the top 3 moves. However, Rg4 is just terrible, it moves a developed piece again (for no reason) instead of developing that pathetic queenside. 1. - Rg4 2. Re1 and black loses another piece, the evaluation is +12 for white.

And it ceded control of the e file to me. Then they went g6 to create an escape route for the king when they should have gone bc6 to block the rook that was coming to e8. Bh6, Rh4, Re8, checkmate. I would have thought Stockfish would have had a better move than just throwing away a pawn, but I guess it can't say "who gives a flip, you've lost".