Youtube, like Facebook, Blogspot, Wordpress, or any other site full of user-contributed content, isn't a source. It's a platform -- same as a (physical) library. What counts is not where the content is hosted but what it is.
A Youtube video of a lecture is no worse than a transcript of the lecture or detailed notes taken by somebody who attended the ...
I personally do not like reading capitalized content - it makes it harder/slower and "screams" at me. Soncino made an editorial choice, possibly in a time where italics or other fonts weren't as easy to use or as common as today, and that choice feels outdated today.
As such I would much prefer to lower-capitalize the text quoted. But it might just be me.
I don't care much either way, but if you do change it please note as much (eg. "reformatted by me" or "changed to sentence case" or something like that). And come to think of it I support adding the "capitals in original" note for clarity if you don't change it. So in short, whatever you do, leave a note.
I agree with mbloch's answer here that the capitalized text is harder to read and is likely an artifact of the typography readily available to Soncino Press. But I'll go further and say that if you substitute boldfacing for capitalization then you needn't even note the difference in an editorial note, since boldfacing is the same as what they intended by the ...
I wanted to make a wiki to combine answers and add, perhaps by category:
Mechon Mamre - Tanach, Talmud, some Rishonim
Vikitekst (Wikitext) - Lots of different sefarim, Talmud with Rashi and Tosefos
Toras Emes (Ateres) - Tanach, Talmud, Rambam, Halacha, Mussar, lots of stuff.
Sources on the Net - Tanach, Talmud, Rambam, Halacha, lots of other categories.