Okay, to sum up....
Disney Security cannot arrest people. They can detain them but they cannot make any arrests. They have no law enforcement powers whatsoever but their relationship with local, state & federal law enforcement agencies probably makes that point moot.
The Orange County Sheriff's Office is the agency that would be arresting him. Disney would have to make a complaint to OCSO and IMO the evidence Adam posted online of himself trespassing would likely fulfill the legal requirements for an arrest warrant and would be introduced into court.
So from that point of view, Disney is being nice here. They haven't done that. Instead, they politely told him he is no longer welcome inside the 47-square miles of private property that encompass the Walt Disney World Resort because he failed to be a properly behaved guest. He needs to suck it up and realize that if he pulls this elsewhere, other Theme Parks may not be so lenient.