While Midway Island does not have a proper ATC type system, it does have radio communication with aircraft landing and departing on the island, a UNICOM.
To receive a ATC clearance one must go to the airport operations office and call Oakland Center on a "land" line telephone. At least that is the way it used to be just a few years ago.
I'm sure having a 777 drop in is a lot of excitement for the folks based on Midway and of course the Gooney birds that call Midway home. Shoot, when I’d drop in for fuel in a Falcon 50 they got quite excited.