In high school wrestling, this is a fairly standard move, though not seen in competitions where the contestants have a bit of experience. It also has no useful application in the world of collegeic wresting and professional wrestling
The Saturday Night Ride is a sloppy attempt at pinning your opponent. It honestly looks like you're trying to boink your opponent. Your arms go under his/hers, to remove their ability to keep their shoulders off the mat. Your torso is on their stomach, their legs on either side so that you can deprive them of that leverage.
My coach would severly punish us if we ever used this against a female wrestler. It is both disrespectful, and since it's useful scope is only against inexperienced wrestlers, it is a sign of sloppy wrestling which would not be tolerated by my coach. (Severe punishment means something like 500 push-ups, 3-5 miles of running, 200-300 sit-ups and probably many many minutes of wrestling against one of the coaches.. to the point, lots of pain)