Most intriguing, I like this thought experiment. I think that if you go by a strict interpretation of the rules, this should be a draw; though I guess I can also see some merit in a "spirit > letter of the law" argument.
Win, loss or draw? What do the rules say?
I get what you are saying, cobra, but I don't think it is that obvious strictly by being familiar with the rules. I imagine there must be some errata laying it out.
Presumably a similar non-ending move would be one that moves an opponent from mating to non-mating material. So if I captured by opponent's last pawn in a bishop vs. bishop endgame, but did not hit the clock in time to complete the move before flag was called, I would lose?

Gee, lubaza, it's a good thing you started this thread; after reading through the responses, I'm truly shocked that so few people (only Crudus and FullmetalAlchemist, so far) understand the FIDE rules regarding this matter!
In this (unlikely) situation, White would win on time. Because Black failed to hit the clock before his flag fell, Qg3+ was never really "played", technically speaking (as Crudus has already pointed out). Therefore, a legal continuation would be: 1...Qh7 2.Qa1 Qb1 3.Qh8#, ending in checkmate for White. The only exception to this rule occurs when a game-ending move is made (checkmate/stalemate/valid call of threefold repetition or 50-moves rule); when this happens, the game is over and the clocks become irrelevant.
Getting back to lubaza's hypothetical scenario, the game would have been drawn if Black had managed to hit the button in time, but then his flag fell immediately after Bxg3 (before he had time to even reach for either of his pawns that could deliver mate). If Black, in this case, had been even faster, he could have won with fxg3/hxg3#, even if he was unable to hit the button before time expired.
Hope this helps
Not entirely true.. A move is chess is "made" after you left the piece on the square (section 4).. A move is "completed" after you pressed the clock, section 6.9 doesn't state if the move have to be completed, and any move done affects the board, this means that the time-out was AFTER Qg3+ and it will be included in the final position.
Think of it like this:
Rule 6.9 states that if you ran out of time but you mated (or any other game finishing move) the mate on the board counts, now if you were able to press the clock you already won on checkmate, this rule exist like this in case you weren't able to press the clock afterwards.. The same goes for any move which is not game-ending, it still counts. The board is always by the last move "made" and not "completed"
This position is a draw, black didn't mate and white can't mate...
It probably doesn't mean much, but I am a certified judge...

I get what you are saying, cobra, but I don't think it is that obvious strictly by being familiar with the rules. I imagine there must be some errata laying it out.
Presumably a similar non-ending move would be one that moves an opponent from mating to non-mating material. So if I captured by opponent's last pawn in a bishop vs. bishop endgame, but did not hit the clock in time to complete the move before flag was called, I would lose?
that depends.. opposite colored bishops and you lose, bishops of the same color it's a draw

Interesting. One would think that the FIDE rules would leave no room for ambiguity. It looks to me like white wins, assuming that moves are only recorded each time the button is hit, and "a legal series of moves" is performed on the current board as it has been recorded. The aforementioned exception is only valid in the case of a checkmate (or stalemate or other legal draw).
Those who would say this is a draw, please provide those passages of the FIDE rules that define the current game position and what affects it (i.e. "making" or "completing" a move). Otherwise, the assumption is that the moves must be completed (the button must be hit) before they are recorded.

I don't know if I'm missing something.
I think White clearly wins, on time.
Black WANTED to play Qg3, but ran out of time before he could complete the move,(by stopping the clock). So he didn't play Qg3, you can't play a half move. So, Black ran out of time in the diagram position, not with the Queen on g3.
Now there are many possible legal continuations where white can win.

I don't know if I'm missing something.
I think White clearly wins, on time.
Black WANTED to play Qg3, but ran out of time before he could complete the move,(by stopping the clock). So he didn't play Qg3, you can't play a half move. So, Black ran out of time in the diagram position, not with the Queen on g3.
Now there are many possible legal continuations where white can win.
Qg3+ does count, the same if you mate and then ran out of time before being able to press the clock.. according to the official rules you get the win, why? because there is a mate on the board, meaning your last move counted, even thou it was only "made" and not "completed", same goes for any other possible move...
Pressing the clock is completing your turn, not your move

FFS, you made me go and check the rules myself. It's quite clear:
6.7 a. During the game each player, having made his move on the chessboard, shall stop his own clock and start his opponent’s clock. A player must always be allowed to stop hisclock. His move is not considered to have been completed until he has done so, unless the move that was made ends the game. (See the Articles 5.1.a, 5.2.a, 5.2.b, 5.2.c and 9.6) The time between making the move on the chessboard and stopping his own clock and starting his opponent‘s clock is regarded as part of the time allotted to the player.
The game ends in checkmate, not one move before it. That means that in the OP example, white wins.

It is a draw. White can not win this one whatever he does, and Black has not delivered checkmate yet. The question is: does it matter that he hit the button after his time ran out or not (since the move was made) ?

And as I can't see how white is gonna checkmate his opponent after Qg3+ it should be a draw.
The point is that Qg3+ is NOT INCLUDED in the position if the move has not been completed according to the rules, hence the bold-face type on "His move is not considered to have been completed until he has done so..." Therefore, the position is such that the white player CAN checkmate the black player by a possible series of legal moves, and therefore, white wins.

Black has not completed the full move of Qg3+ in time so white can simply claim flag (Qg3+ has not actually been played)

And as I can't see how white is gonna checkmate his opponent after Qg3+ it should be a draw.
The point is that Qg3+ is NOT INCLUDED in the position if the move has not been completed according to the rules, hence the bold-face type on "His move is not considered to have been completed until he has done so..." Therefore, the position is such that the white player CAN checkmate the black player by a possible series of legal moves, and therefore, white wins.
But the only legal series of moves does not lead to a white checkmate. Since the player released the queen on g3 it is the only legal move for black. I vote draw.

Well the rules need to be more specific on a move being "made" or "completed" because that is the problem.
If ...Qg3+ counts it's a draw then and if Qg3+ doesn't count then White wins.
I don't think it matters very much, since black already touched the queen and placed it on g3, and then released his hand. Qg3+ is the only legal move he have ( according to 4.3 and 4.6). this is why it is counted as "made", since it's the only legal move now even if it's not completed by pressing the clock.
anyway I asked an International judge, still waiting for his response.

My intention with the opening post was actually not to discuss whether Qg3+ should count or not, but that's OK, it has turned into a very interresting discussion anyway.
Ironically, just after I started this topic, I lost an OTB tournament game on time, it hasn't happened to me in years

If you'll think about it whether Qg3+ should count or not is the answer to the original topic.
Either it counts and it's a draw, or if doesn't and it's a win for white.
Gee, lubaza, it's a good thing you started this thread; after reading through the responses, I'm truly shocked that so few people (only Crudus and FullmetalAlchemist, so far) understand the FIDE rules regarding this matter!
Ah-hah. The well-known (around here anyway) "everybody's stupid but me" approach...
That's not true at all. Now, before you start accusing... the "surprise" wasn't that players didn't seem to know all of FIDE's laws, but that there were so many stronger players that were uncertain how to answer the OP's question. Perhaps I'm just a geek when it comes to all those boring FIDE rules and regulations that no one else cares about...
"Uh-oh (looks like cobra strikes again)" (#26) - Jeepers! The next time I try to be helpful, by answering somebody's question on the forums, I'll consult you first to make sure it's okay
"Nobody's immune from that feeling, my friend (except maybe guys like Alboz)." (#22) - And now you're comparing me with the likes of AlbozAlbaner... where'd I go wrong??