Perhaps the simplest definition I can come up with for completing a game is "a favorable dead end". It's a dead end because TASes are about entertainment and at the finished state, no further input should show the viewer something new. It's favorable to exclude "fastest crash" and "fastest death" runs.
Note that I'm not saying that input is no longer read or accepted. It's just that new input shouldn't show the viewer something new. The viewer should get a sense at the end of the video that "something good has happened". That might be as simple as a "THE END" screen or as vague as looping back to the first level. The important thing is that further input will not advance the game to a novel state (given the run's restrictions, e.g., 100% vs. any %).
It's the matter of defining or even merely recognizing "favorable" and "novel" states that makes this difficult.
Let me cook up an example. Star Fox was mentioned, and I think it has some interesting properties. With the slot machine ending, after the letters in THE END have been oriented upright, there is nothing meaningful to show the viewer. I would argue that the game has clearly reached a state where no more input will be novel, even though the game still accepts input. The real gripe here is that the state isn't really favorable, since enemies continue to attack you occasionally. Eventually, they kill you, you return to the start of the level, die repeatedly until you run out of lives, and then get the bad Game Over screen.
On the other hand, let's look at the "standard" ending. It's a little Easter egg that if you wait on the "THE END" screen for about ten minutes, the game plays a cute little reprise of the main Star Fox theme a few times. I can't find a video of it online and I certainly can't find it in any encodes because no encoders want to record an extra ten minutes that most people won't be interested in. Nevertheless, the game's state does progress. We even have
some examples of this.
Well, that's really more of aesthetic choice by the encoders, isn't it? But suppose that music could only be triggered by pressing a button. It's just a little Easter egg tune that requires one button press, but it does put the game in a novel state. What should we do in that case?
I don't think I can weigh in any more than that. I believe it ultimately comes down to a broad consensus and/or the opinion of the judges on a case-by-case basis (which is really what we all know and are saying). Nevertheless, it may be worthwhile to frame each case as a question of the favorability of the ending and the novelty of further input.
