Sure. What you need to do is make the segments where the user has a choice into menus, with the video as a background. Set the end action of the previous video segment to link to the menu. If you don't want the buttons visible, simply edit the menu in Photoshop and turn off the visibility of the layers inside of the button's layer set (as long as they're named correctly, Encore will still treat the layers as a button) and delete any highlight layers for the button. You'll probably also want to set the buttons to auto-activate. Finally, link the buttons to the next segment of footage.
Once caveat to keep in mind: By DVD spec, the amount of data allowed for all menus on a disc is limited to 1 GB. To my knowledge most DVD players don't enforce that, though, and I don't think Encore does either, but it's something to keep in mind.
The reason why i asked the question in the first place is because of the 1980's arcade game Dragons Lair. You can get the game on a DVD and its the same as it was in the 80's. You choose where the game goes by pressing your DVD remote buttons. I dont know if any of you guys have played it but if you dont press the button when you are supposed to it cuts to a scene where you die or whatever. And it way over 1 Gb the whole game. Maybe they used a better Authoring tool, the game was made back in 2002 for the DVD. I will try the tips you have gave me as i dont think mines going to be that big, i just wanted to know how its done for a little video.
Ah, yes, I remember Dragon's Lair quite well. It sat back in an oddly well-lit corner of the arcade, and I dumped many nickels into that old LaserDisc-based machine. Pity that I was never really able to get more than a couple of levels in. My brother had good luck on the Commodore 64 version, though of course the graphics were junk compared to the video in the arcade.
You're on the right track for your own game. If you keep your animated game segments short, and all the animations (success, failure, transition, etc.) as timelines rather than menus, you'll probably be okay.