It's because the black king is not check, but can't move anywhere either.
How is it not check though? Any move it makes I can either take it out with the queen or bishop.
Which is why it can't make any move at all. The rules of chess dictate that no player can move a king into a position where an opponent's piece could capture it.
That's not the same as being in check, though. For a king to be in check, there has to be a piece that is
currently in a position to capture it. In this scenario, the black king is not in check because no white piece can currently take it. But it also can't move, because any move would put it in a position where a white piece
could take it.
Thus, stalemate.