Can black win in this KR vs. KN endgame? If white has the next move, can black still win the game? The players accepted the draw here, but I am not sure if it is still a draw.

[fen "8/8/3k4/4NK2/8/8/8/6r1 w - - 0 1"]
No, this is a draw. These kind of positions can be checked with an online database, e.g. this one.

In general, King+Rook vs. King+Knight is only a win for the side with the Rook if the other King is cornered or separated from its Knight, as also described in this answer. Just play around a bit with the endgame database to get a feeling which positions are drawn and which ones are won. Black to move wins in this particular position only because of some short term tactics (Rf1+ and Re1+ wins the Knight).