Having a kid react to something is an incredibly superficial similarity.

I agree. But the creators of the content felt that it infringed upon their work. Maybe not enough for lengthy and costly legal recourse, but enough to go "this sucks".

I personally probably would have loved the exposure, but I'm not the Fine Brothers and I don't know how they personally feel with regards to Ellen.

DID they ever go after Ellen legally? I don't recall they did.

I don't think "Ellen" stole anything. I don't think she even knew who they were before doing the show. I don't think the skit was even her idea. Some producer or writer probably put the idea up, people thought it was good, it tested well, it got put on the show.

I don't think anyone tried to "steal" anything. But if the content creators feel like a work, even one made in earnest, infringes up their own work to such a degree that it might cause problems, dilute their own brand, etc, then they are right to not be okay with it.

What exactly is unique to the Fine Brothers format?

One of the issues with how the trademark system of the US is set up is that this question is hard to answer, simply because there's no standard. There are no written rules set in stone about what something so abstract as a concept as this actually means. Eventually it comes down to the "feel" of the show. Cuts alone won't do it, editing alone won't, commentary won't, etc. It all adds together.

I have no idea what content you watch, but you might agree that they have their own sort of styles and feels to their shows. How they edit, cut, position, interact, etc all comes together to create their specific "feel".

The Drunken Peasants podcast also has three or four people reacting to videos, and nobody would say they're stealing the Fine Brothers format because of it.

Exactly. It's not the same feel.