Generally, we try to ensure that puzzles are entirely contained within the StackExchange site. This is because there is no guarantee that any external site will continue to exist. We want the puzzle to be just as accessible 20 years from now as it is now, but if it depends on external resources, there is no way to guarantee that.
This hasn't been a hard-and-fast rule, and there certainly have been puzzles that do use some external resources, but it is not encouraged.
In your case, I think the main issue is that the entire puzzle is elsewhere. You're not just including a resource as one piece of the puzzle; the entire puzzle is the resource. That means that for someone who may be behind a firewall with no access to YouTube, or who doesn't have the capability of video playback on the device they're using, there is essentially nothing of value in your post.
There doesn't really seem to be any effective way of implementing video puzzles at this point in time. They unfortunately just aren't a fit for the StackExchange format. There is the option of using animated GIF files, but that may or may not work, depending on the video.
(As an aside, some StackExchange sites do have the ability to embed YouTube videos (Movies & TV and Science Fiction & Fantasy are two that come to mind), so it is technically possible, but not enabled on Puzzling.SE.)
