Looks like an add-on is interfering. Please click Tools > Add-ons, disable all add-ons, re-start the browser and try again. If everything works as expected, you can re-enable add-ons one by one to find out which one caused the problem.
This is to be expected, because if a video needs a plugin such as Flash, it won't play in TenFourFox anyway, no matter which add-ons are enabled or disabled. Do you still get messages about "domain restrictions" for most videos?