Because it's not copyright infringement. Copyright applies to the content (i.e., DVDs, videos, or even simply clips of larger videos). Fanfiction is not (usually) copyright infringement because ideas can't be copyrighted, only the distinct expression of the idea can. (Without going down the rabbit hole, Captain Kirk is an idea, his portrayal in any particular tv show or movie would be the expression of that idea).

The video is disclaiming trademark infringement, which is not a crime.