The increased file size was "due to the increased amount of content" at launch, including map files for Warzone, as well as the Zombies mode, and the fact that a lot of content from Modern Warfare II carries over to Modern Warfare III.
The file size of Call of Duty: Modern Warfare 3 is well over 200 GB on consoles and PC due to a variety of content install packs, including Warzone files.
It likely comes from the idea of "scooping" up a story before others, as if using a scoop to gather the latest information. The term has been used in this context since the early 20th century, when newspapers were in fierce competition to publish breaking news before their rivals.
In American football, the scoop and score is a defensive play where a player picks up a loose ball from the ground and subsequently scores by running it into the opposing team's end zone. This type of play may occur when the ball is fumbled by the offense or mishandled in some way.