It's unfair to just say "Hey look. Youtube and Vimeo with billions of dollars and decades of experience between them decided to put a volume control. You should too." But personally, there should be a volume control. It is very common for multiple streams of sounds to occur in today's computing environment. I could have a Youtube video going for the visual component and some other music. Or, maybe I want to leave the speakers on at the maximum volume for notifications but not have this music completely blasting as a consequence. (This is not a far-out edge use case).

I love the minimal look and the thought that went into the design. I will definite check it out further. It will be interesting how you fit the volume control into the component which at the moment looks really well balanced and laid out. (ie. How you might improve the already-excellent UI by adding something to it)