I saw both forms where the nickname of an user is used as an adjective, but which one(s) are idiomatic and why?
Both are idiomatic and essentially mean the same thing, although the name "PewDiePie" is being used differently in each.
"PewDiePie's videos" means the videos belonging to PewDiePie. The videos are his work, he created them, so it is correct to refer to them this way.
However, a noun can also be an attribute of something. When it is used this way it is called an attributive noun and acts very much like an adjective. You are differentiating the videos from other videos by attributing the artist's name to them.
Did you hear Coldplay's new single?
Did you hear the new Coldplay single?
Both of these are also idiomatic.
This is a can of Coke.
This is a Coke can.
This is a video of PewDiePie.
This is a PewDiePie video.
When something is a brand name it can also be used as part of the product name. "PewDiePie" is a brand name of sorts, not because it isn't the star's real name, but because it is a name under which he has become famous.
There is a subtle difference in meaning.
"PewDiePie's videos" has more of an implication of "all of them". When you use the "X's Y" construction, the meaning is definite: it is usually equivalent to "the Y of X" (in this case, "the videos of PewDiePie", although that wouldn't be an idiomatic way of putting it). Because "watching" is a progressive form, "I am watching PewDiePie's videos" doesn't necessarily imply that you have gotten through all of them, but it might imply that you plan to eventually watch all of them.
In contrast, "PewDiePie videos" is indefinite, and would imply "some of PewDiePie's videos". I find this to be the more idiomatic choice.