All the other dissatisfaction is from Ketch (sorry, but really you're the most indignant again)

Well, that's just how I am :)
You know, on the Portal I always cited the AK on HeroesWorld as an example of how controversial situations should be handled. I even suggested creating a similar body there, but it hasn't been created yet. But in this situation, I am simply surprised (stunned, amazed, shocked, flabbergasted) (pick one) by the unprofessionalism of the AK.
What do we have? The recording and your testimony, the fact of the game, the absence of complaints from Player2 (confirmed by the report), Player1's explanations, and Guest's testimony.
The recording is the strongest argument. Without it, there would have been nothing at all.
Player1's testimony explains that such a thing could have happened, but he is not aware of it because there was Guest, who stayed at the computer after he left. This is confirmed by Guest. In contrast to their testimony, there is your testimony that the mouse was moving in Player1's style. Fast and confident. So Guest moves the mouse slowly and with the cursor trembling across the screen? Well, never mind... You have no more arguments in favor of Player1 moving the mouse rather than Guest. And the recording does not show the moment the mouse was handed over. You yourself wrote that you started recording only after the codes were entered and the save was loaded. That is, the moment of the mouse handover cannot be tracked from the recording. So we have your testimony, based on the mouse movement, that Player1 was playing, and contradicting testimony from Player1 and Guest that Guest was moving the mouse. Well, sorry... No unbiased court would render a verdict of "guilty" based on such arguments.
Okay, but there is a recording of the codes being entered. What to do in that case? The save was opened. The rules prohibit it. Although it doesn't say that other people are not allowed to open it. There are no complaints from Player2 at the time the game ended.
You could simply turn a blind eye to it, but take note of the situation and quietly but closely monitor Player1's future behavior.
Or, show principle and give him a technical loss for making a mess at his computer and warn him that such behavior is unacceptable. If it happens again — an immediate and unconditional disqualification.
But, definitely not a ban or removal from the tournament. Since the fact of Player1 cheating was not confirmed.
If the AK had made such a decision, then if Player1 is indeed honest, he would never let any guests near his computer again, and Guest himself would never sit at his computer to look at his saves if he does not wish Player1 ill.
If Player1 himself cheated, then sooner or later he will still get caught. And then, on completely legal grounds, given that he had been issued a warning, he receives a disqualification.
In general, this is exactly the procedure for reviewing controversial situations that is practiced everywhere. I have not judged or conducted online tournaments, but in offline tournaments I caught several cheaters this way. And the situation was settled amicably. The person was banned, and neither he nor anyone else had any complaints against anyone.

P.S. I am not personally or virtually acquainted with Player1, Player2, or Guest. I have communicated a little with the Witness a few times on ICQ, and even then mostly offline. My attitude toward the resources they represent is evenly benevolent. On this basis, I consider my opinion to be completely unbiased.