The linked topic gives good reasons to explain the sense behind having things aligned left in the browser.
A few other things to consider:
Looking at your 1920x1080 screenshot there is a lot of white space. However, that is not neccesairly white space that could be used otherwise. Imagine the whole page being filled on your HD screen and the page would overflow with information, lose all hierachy and be hard to navigate. Most people with big screens sizes don't actually browse with equally big browser sizes. Most likely, users on spacious devices have a view that comes closer to your second screenshot, with an almost centered impression that just gets more firmely attached to the left side with solid navigation elements.
The other thing worth considering is the content that is shown. Considering youtube shows videos, it does not make sense to have a featured video at very high width (certainly not in the preview thumbnail) even though the user's device could show it, because that would increase the video's height in a way that all other content gets pushed beyond the fold. Limiting the thumbnails to a size that allows for a bunch of content on any page also means that the over all column size stays limited, unless you would fill the whole screen with thumbnails, and I already explain my though on why I don't think that is a good solution either. Thus you end up with a limited width layout.
