I think it might be a red herring to get into an argument about "when the game is over" because this is simpler than that. What we're trying to agree on is terminology.
The question is, what does "reaching the kill screen" mean?
Jumpman gets killed by a timer bug approx. seven seconds into the 117th board (L22-1).
The question is whether the term "kill screen" refers to the board on which the event happens, or to the event itself.
From what I understand, what Ken is saying is that there is no stage/board that "is" the kill screen. In other words, it's not correct to use "kill screen" to refer to L22-1, but rather to the event that happens on that board. By this definition, you have not "reached the kill screen" until Jumpman dies from the timer bug.
Others are saying that "kill screen" is an alternate name for the 117th board. So, a player has "reached the kill screen" the instant the L indicator goes to 22, since, by that definition, the kill screen is a level and not an event.
The latter is the impression I've been under up to now. I thought "kill screen" in Donkey Kong's case just meant "board 117," as opposed to "Jumpman dying due to the timer bug on board 117."
I don't care which meaning of "kill screen" wins out. But as long as bounties are involved, everybody's gonna have to agree on one!