We should note that this doesn't mean Modern Warfare III alone will take up 200GB of file storage though the base installation for Call of Duty HQ (the central hub needed to access Modern Warfare II, Modern Warfare III, and Warzone) is roughly 50GB.
However, typically, Call of Duty Mobile requires around 2 to 3 GB of internal storage space for installation. It's worth noting that the game's size may increase over time as updates and additional content are released.