He’s not. That’s why they mention his name in both commercials he’s in. In the one the OP is discussing, he’s wearing a shirt with his own name on it, AND he plays it (as a verb) in the faux Scrabble game.
Exactly. I think you could also draw a comparison to playing Scrabble with a gay friend, then spelling out the word “faggot” on the board. Geico might be poking a little fun at gay culture.