Update #1: New working link has been added.
Update #2: Aaaaaand it looks like Ubisoft have shut down the videos we've found. Feel free to email us if you find working links and we'll update.
Update #3: We've added a fresh link from a new source of different in-game footage
Somehow (don't even ask because we have no idea) YouTube user eaglesblades has gotten himself a copy of Far Cry 3: Blood Dragon and put it up on youtube for all to see. I'll have more as time goes on but you can watch the first bit of the 80s VHS Sci-fi for yourself.