Weird situation. Yeah, I think playing to king capture instead of mate resolves all the complications about who wins, who gets points, etc., in both teams and FFA. This is just another such case.
In that case, you would have been able to take blue's queen with your king, and then blue couldn't escape yellow's queen.
First yellow mated blue, then Green just played Qxg2 and it's mate, since I had no valid moves. However, there is a bad logic to this. Yellow had previously landed mate against blue, and actually made an unavoidable checkmate first, and would also execute a capture of the king first. I know it's supposed to be possible for the team to help out, but here it seems we mated first, but since I was in turn first, we lost, because the "empty moves" had to be played out. I would rather see a king capture to finish the game, then the first to mate actually wins....