After watching the second fan clip from above, and slowing it down to the max speed and pausing it when Max first starts exending his arm, Egener's arm is already bent and raised as he prepares to throw a huge punch.
By the time Max has his arm fully extended, Egener not only has right arm above his head about to punch Max, he has also grabbed Max's shoulder with his left arm.
At no point does Max clench his fist. It is clearly not a punch. It can't even be a push or a slap.
For me, he's spotted that Egener is about to punch him (maybe due to something Egener has just said) and he has raised his arm in defence.
From that, Max correctly got a match for returning to the bench after being thrown out. No further ban required though.
Can't see why Francis got his match though - should be rescinded.
Egener has skated halfway across the ice to restart the trouble and attacked two people off the ice. 3 Games at least for me.