Well, there are multiple things going on. First is the franchising thing, which, whatever, they can license out their logos and so on if they want. Second is the trademarking thing, which leaving aside the issue of overreach given how long reaction videos have been a thing, might not in itself be a major problem if we didn't already have reason to suspect it's going to be abused.
Third, and worst, is the "format" thing. We don't know exactly what they consider their format--the most they give us is telling us to watch one of their reaction videos and it'll be obvious. So we're left to guess. We've seen from their past behavior that they consider something like
Ellen's segment or the
Buzzfeed video to be very similar to their shows (I've watched both, and the main similarity is the generic idea--multiple people from a particular group being shown something and describing their responses to it, with cuts between the interviewees). Obviously their twitter calls to arms don't mean anything legally, but it's strongly suggestive of their mindset and what they will try to do--they feel that they own the generic idea, not just their branding. In combination with the first two things, it's not pretty. Put all together, it looks to me as though they'll pressure smaller channels that run similar content to come under their banner, using their newly-acquired trademarks and Youtube's overeagerness to take things down as a blunt instrument. They don't even have to actually take down channels as long as they have the implied threat at their disposal.
Is that definitely what's going to happen? Am I perhaps being unfair here? Maybe. On the other hand, looking at the Seniors React thing, it kind of looks like they've already done something like that.
There's also all kinds of tertiary stuff around, like, the irony of them being so uptight about content when their whole model depends entirely on using other people's content, or them deleting comments, or just generally coming off as sleazy jerks, but that's less important. It wouldn't be a big deal if not for the above problems.