I think it's just our widescreens. I like pages that are coded to stay in the middle, because usually if a page is coded to cling to the left, there's that big empty space on the side you depicted here because my computer has really dramatic widescreen dimensions. It sucks. :-/ I don't think it's Youtube's fault really, it probably looks normal on most computers.
I think it's more of a poor attempt to integrate youtube in google services. Same waste of space can be found on Google+ account, and on facebook, but you don't notice it on facebook because the content is in the middle and the waste space is split in 2 half, left and right.
And if design is poor, engine is worse, "Recommended for you" videos are always the same, drives me crazy.
It seems to me like someone at YouTube made a mistake because channel pages are still centered. So maybe this huge monstrosity of a white space is just a mistake? Who knows if they'll ever get around to correcting that.
I swear if i were in youtube corporation or whatever i will walk up to them to change it back that everyone is tire of this new layout changes and so am i i'm considering this an absolute garbage the old ones are fun that the new one's lack of.
I honestly like the new Youtube design, but there are some things that ruin it, like puting everything below the video instead of having the title, subscribe button, and some other things above it. It just makes the bottom of the video look so crowded and above it looks so empty.