It's not sporting, but on this site it appears to be pretty normal. Don't let it get to you. You're going to read lots of threads complaining about the lack of sporting behavior, the failure to resign, blah, blah, blah. Really, big deal.
For instance, I had a game where I offered a draw twice and the opponent rejected it. Then when we got to an absolute dead draw --that is stalemate in about three moves--he stopped playing. In another game my opponent could make only one legal move, after which it was checkmate. He stopped moving.
In both of those instances I made conditional moves. You'll see that button available to you when it's not your move. Just make the move that your opponent must make or will most likely make and then make your reply. It it's a forced mate in 4, for instance, just make the moves that force it, close the window and forget about it. As soon as they move on their end (if they do), it will trigger your response automatically. You can be sunning on the Riviera.
Above all, though, just roll with it. Most players on this site are sporting, polite, and relatively mature. Others are whining little babies who pick up their toys and go home as soon as things turn against them. Don't lose any sleep over it.
An online game I was playing just 'finished', because the guy let his time run out. This is turn-based correspondence style chess, and we had a day or two for each move. It was forced mate (on him) in one move. Obviously if he didn't want to endure the checkmate, he could have resigned. But just to let the time run out? I mean, please acknowledge the time we had invested in an interesting and challenging game, by at least resigning if you dont want to see the checkmate. Thats what i would do. The material was close and we'd gone 48 moves at this point.
I'm new here, and have only played about ten games, so I do not know the etiquette.... Is this normal? Doesn't seem like a very sporting move to just let it time out when you are about to be mated.