I love that clip!
The original was actually a Trident SLBM launch. It can be found
here.
In some ways, however, it has a basis in reality.. and more fiction.
If you remember the Gerry Anderson productions series UFO, it had a submarine with a fighter aircraft on the bow - Sky 1. It launched like that.
Also, during WWII the Japanese experimented with having aircraft kept in hangars on submarines. The sub would surface and the aircraft would be catapulted off. Not that successful, and only about 3 of them were built IIRC.