Surely the flight attendants politely asked the man to leave, and when he refused they called their manager who did the same, and only at that stage did they call the police, who also probably asked the man to leave first, before finally resorting to dragging him out.
At the end of the day, the plane is owned by United, and they have every right to uninvite him from their property, at which point he is trespassing, and it becomes a police matter. Sure, they might violate their own ToS on their tickets at that point, but that's a purely civil matter.
Maybe, maybe not. Airlines are heavily subsidized by the US government in exchange for regulation so they will offer service to rural areas which might not otherwise be viable to run an airline into our out of. There are also laws and regulations which turn disobedience of airline personnel into a federal offense in particular situations.
Whether these, combined with this passenger's situation, turns this from a civil to a federal matter is something I'd leave for the lawyers.
The objection here is that violence wasn't sufficiently gated, and nor was violence minimally applied -- the airline could've just paid people to get off with a real offer, and not a dishonest offer where people suspect they're going to get tricked by funny coupons and vouchers.