Sorry if this has been resolved in the 20-some odd pages of this thread. Regarding OP's video link, I prefer this one instead due to Magus being actually in the party which clears up some confusion.
http://www.youtube.com/watch?v=8c2OnkfNK0MMy take on it is that when Crono & co (with Magus in toe) arrive on the scene here, they are encountering "600ad Magus", the Magus form the alternate (original?) timeline in which Lavos was successfully summoned by Magus at his castle as would have happened if Crono and party had not interfered. 600ad Magus doesn't seem to recognize them (from his point of view, it is the first time he's met them), but he quickly deduces what's happened based on seeing an alternate version of himself with that party. As happened originally in that timeline, when he attempts to engage Lavos alone, he is promptly slain. That is the end of 600ad Magus. The Magus that we see later in the cutscene is actually the present timeline's Magus, the one that was in Crono's party moments before. Being slightly older and much more powerful (600ad Magus was only approximately level 35), he isn't completely slain by Lavos' onslaught, and through force of will, pulls himself together long enough to have the dialog with Schala we see in that scene.
It is THAT Magus then, that loses his memory that we see in Radical Dreamers and Chrono Cross.