It was just called The X-Files Game, so the first one I guess. It was point and click with full motion video. I don't remember ever having Scully killed when I played, though Mulder ended up dying a few times.
Fact: at one point in the PS2 game, there is a sequence where you have a briefing in Skinner's office, he leaves, then reenters dressed as a Nazi officer and fights you.