I Bought a Game from the iPhone App Store, and I Installed it on my Macbook from the Mac App Store? I bought "Castle of Illusion" on my iPhone, and I am signed into my iCloud with my Apple ID and such on my laptop, and downloaded the app in the Mac App store. I pressed "Install" and it said "Installing". Did I just BUY the app AGAIN? Is it linked with my iPhone apps?
App Store on iPhone or in iTunes is specific to iOS. If you are buying an application from there will run on iOS devices only, not on OS X. Similarly Mac App Store is exclusive for OS X apps. You cannot buy an app from App Store on iPhone and transfer it to Mac App Store. Both apps are incompatible with each other.

In your case, you bought the apps separately for your iPhone and MBP.