This is the reason I have completely deactivated any screensaver or powersaving modes on my computer. What if I'm proofreading a paper, or examining a picture? I'll determine when my computer is not in use based on whether or not I'm using it, not on whether a timer has run out. If I'm done with my computer for more than a few minutes at a time, I just turn off the monitor. I've only forgotten or neglected to turn it off a few times within the past several years.
If you want to keep your screensaver, there's probably some setting somewhere to tell the machine when you don't want it to activate. It might be in the Control Panel, or possibly in the settings for your video viewing software. If that doesn't work, you could just turn off the screensaver before you watch a movie, and reactivate it when you're done. Just hit "Apply" instead of "OK" to keep the window open so you don't forget to turn it back on.
Are you watching the video in a window, or fullscreen? If for some reason you're not using fullscreen, try that.