There is no GameMaker Studio Master Collection specific download.
There is currently only:
- GameMaker: Studio 1.4
- GameMaker Studio 2
With Studio 1.4 you enter your Licence key and it authorizes and makes available all exports associated wit your key. With Studio 2 you login via within the IDE and then all licenced exports are made available.
You can download either by losing in to yoyogames.com and selecting Download from the GameMaker dashboard choice.