Have you compared Flash browser pluggin versions between working machine and non-working?
IE main menu... Tools/Manage Add-ons/... look for "ShockWave Flash Object" and compare versions.
All users are on Flash version 126.96.36.199
Yeay... too bad about using the 11.2+ version. This example may be another good reason to NOT always update to the latest version of anything... software or browser pluggins.
On other users machines, the .SWF does not load correctly. There is a big white spot where the .SWF should be. If you put your mouse where the .SWF would be and right click, you see the pop-up menu for the Flash player.
If the .swf is loading, then the problem may be with the video file.... the .swf loads but cannot load the video file. Can you verify that the .swf is downloading? Have you tested using IE Developer Tools:
Perhaps the "Profiler" tab could verify what is downloading.
It's tougher now to access and view the Internet cache files like you could with XP. That will verify exactly what is downloading and what is not.
Can you do a little testing with FireFox just to verify if it's the machine/network or just the IE browser on that same machine?