Following my research I don’t think it is possible to have interactive video within muse. Alternatively there is more room for interactivity throughout the site with different widgets.
Interactive scale widget:
This widget allows simple state changes when clicking or hovering on a button. Whilst this isn’t a massive level of interactivity it does add an extra level of depth and could work well when applied to the right elements.
http://resources.muse.adobe.com/products/interactive-scale
Flashlight 404 widget:
This widget adds an editable 404 Error page with an interactive flashlight effect. Whilst it is highly unlikely that a user will 404 on my site it is a good failsafe and users will likely appreciate this interactive novelty.
http://resources.muse.adobe.com/products/flashlight
Animation Effects Widget:
This widget allows the user to add 95 different customizable widgets that add some level of animation and interactivity to the site. Solely visual it can make the site a lot more interesting on the eyes for the user.
http://resources.muse.adobe.com/products/animation-effects
Movable Item Widget:
This widget allows the user to add a movable box on screen. I believe this could work well with some of my ideas if I’m able to frame other objects inside of this item.