Is it technically possible to make a self-destructing movie clip?
Solution 1:
Yes. But you need to be aware that this behavior is not intended by the developers of file viewer programs and is seen as malicious, not routine, expected behavior, like shown in some movies.
Bugs in viewer programs for media and document files have been abused for a long time. Maliciously crafted files exploit these bugs to execute other code, that could also delete that file that is being viewed.
If you read about security vulnerabilities e.g. in Adobe Flash, Apple QuickTime, Windows Media Player, or Adobe Reader, quite often this is what's meant.
The simplest exploit of course is to crash the viewer, but more sophisticated ones are possible, given enough time and/or money to develop them.
This depends, of course, on the exact environment (viewer program and version, OS and version, etc.) the file is viewed on.
Publication of such a file/exploit would likely lead to the security vulnerability being patched.
Solution 2:
If you were to roll your own, how about a streaming client that runs only off a proprietary boot cd? That way it could monitor what other processes are running and die if anything unknown (which could be a screen grabber) is also running. Not sure if it could tell if it was being run within a vm, but it should refuse to run if so. The client would stream a limited buffer of data with no pause or rewind control, and would not cache to disk ever.
This could be a stand alone appliance which could be built hard-wired to "melt-down", even literally explode(!), at end of playing.
Can't beat the external camera recording, though. Except maybe with lasers...