There would be no outlets on the island for power for the TV. (It is a dream, however.)
No explanation was given for where the Howells and Ginger were when Alf was on Gilligan's Island. Seems unlikely Alf would not even ask. Actually he did ask, and was explained to by Gilligan that the Howell's built their own resort on the other side of the island, and Ginger went off to live with them them and they don't let the others in there much.
There was a movie called castaways on Gilligan's island were they were all rescued for good so they would nor still be on this island. however, this a dream alf is having and its possible he never saw that movie. if he had seen that movie he would for been talking about it like he talked about the show all the time.