Absolutely not. Simple games can be fun. Games aimed at children can still be fun. Games with no serious themes, blood, nudity or violence can be incredibly fun.
It depends on what you mean by "mature". If you mean it in the sense of "Mature Content", then no, of course not. Portal 2 has no blood at all (well, I suppose when Chell gets hit by the turrets, there's a bit of blood), and you have nothing but a portal gun. There's no swearing, no gore, no real violence except smashing a few turrets. It's rated PG and it's one of the best games I've ever played. Ever.
Super Mario Galaxy, Tetris, Civ V, Picross 3D, the World Ends with You and just about any Racing game under the sun have no blood or gore or nudity, and yet they are some of the best games made in my opinion.
If you mean mature as in "adult themes" and subject matter and aesthetics... then it can help in some cases, but it isn't required. Again, Super Mario Galaxy is plenty fun and it has no adult themes or complex messages.
There's a time and a place - we all like deep, meaningful films like "Eternal Sunshine of the Spotless Mind" or "Synecdoche New York", but we certainly wouldn't want all films to be like that. We need our "Independence day" and "Iron Man" films, but again, we wouldn't want all our films to be like that either.
A game with mature elements can be good. But we don't want every game to have them and a game can be perfectly great without them.