[Schrödinger]

If Br was missing just ONE electron it would be called a Free Radical; and would end up attacking the H on the methyl instead.

Since Br is 2 electrons short, it makes sense that it attacks the double bond on the aromatic ring, and then the rest of the rxn follows as showed in that flash.

A free radical is just a neutral atom. There are no electrons missing.
FeBr₃ is a Lewis acid (accepts a pair of electrons). So, it causes Br₂ to split into Br⁺ and Br^-. Br^- is accepted by FeBr₃, since Br^- is a Lewis base.

Why does it refer to Br as Br+ instead of Br 2+ in that case?

So, after Br₂ splits, what's left is Br⁺, because Br^- is accepted by FeBr₃. This is what attacks the electron rich benzene ring.