No, he shouldn't have quit. It was still a playable game.
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Here's a game, I was black:
https://www.chess.com/livechess/game?id=1460908768
At this point white quit... I would have taken second black rook and continue playing. White would have two rooks and I would have a queen, material even. So, is this quittable or playable?
(oh and I'm aware I made mistakes, but I'm not looking for that analysis, just opinion on quit/play)