If it was a short story (and not a TV show or movie), I would have suggested "Don't Look Now" by Henry Kuttner. This story may have been inspiration for an episode of something, but I'll leave it to someone else to find (I don't know where to start on that...)

A comment, because these are not answers to what it is or might be, but some things it is not. "Better Than Life" by Grant Naylor features the headset you can't remove forcibly, but not the other features (I don't recall the girl being killed as part of it). "Space Demons" (and at least one of the sequels) by Gillian Rubinstein features 'going into the game', but not via a headset. "The Dreamland Chronicles" (a trilogy) by Wm. Mark Simmons features life-pods, not headsets for the VR aspects.

Was the book new at the time? I ask because "Mirror of Her Dreams", published in the 1980s, which might match (depending on how accurate the description above is).