I'm going to assume that he's joking, given the context of the story. His Gulliver's Travels comes out soon (now?) and apparently there's a line in there where he calls himself Shakespeare (at least, that's what my kids keep telling me). So I'm sure that came up during an interview and hence the above quote.
Although it does make me think of a question. Who among modern actors could play the great comedies? What actor working today would we like to see as Feste, Jaques, or Bottom? I deliberately leave Falstaff out of the list, because I think he's a category all to himself.