No, one could make the argument that that is fascism, but not socialism. Socialism--or more specifically, what is referred to in the article as the "New Deal"--is an economic/social principle.
I can understand a person disagreeing with federalizing the baggage handlers, and I personally think idea of letting the states take this one on is better. But even with that angle of criticism, I don't see how a person could assert that Bush is now a "New Deal Democrat." It makes no sense to me. And I’m no Bush apologist.
I am assuming that he meant airport security. Many do not realize that those rent-a-cops were IN FACT government employees prior to 911. Airlines do not provide security the airports do. Airports are governmental entities and they have farmed out security to a few security firms. The real fact is that Bush did NOT want to federalize the security workers in the first place. He wanted to establish federal guidelines to standardize the national network. He lost, and rather than not do anything he signed the bill that federalized security. The situation as it now stands is that airport security will be under the Homeland Defense agency and he is threatening a veto of the HSA act if he does not get relief in weakening civil service protections for all employees within that agency.