There has been a trend lately with you tube where you need the app for your device to view the vids. There is a version for both android and iphone's that should fix that issue. Not sure about other types of tablets.
The app is what has messed it up. Months ago, after getting this same message many times, I'd found a tiny link at the bottom of the page (both Youtube and Vimeo had one), saying something like "use desktop." Vimeo still has that, but Youtube doesn't. Youtube has been experimenting tho- making lots of changes on an almost daily basis sometimes. I think they forgot to add that back in. Next time they bug me for feedback I will mention it.