Mike played guitar in a few of his other performances, so he knows how to play. Last night, I think he was just doing the rhythm guitar/chord changes while Casey was playing lead, though.
Anyway, no it's not a requirement to play an instrument for the show. They actually just started letting them play instruments in Season 7. But it does help to be able to play an instrument,though, because the ones who do seem to last longer in the competition than the ones who can't. Since they have to sing other people's songs, being able to play an instrument and interpret the songs their own way kind of separates the good Karaoke singers from the real artists to most voters, I guess. I don't really care either way,though, because it is a SINGING competition, after all. But as long as someone can actually sing well, I guess it doesn't hurt to be able to play an instrument too.