shouldn’t the game be installed in /mnt isntead of home
No.
The symlink creates a link between /home/Games/SpecificGameWithAnIssue (dir1) and /mnt/DriveTwo/WhereTheGameNowLives (dir2). Anything you put in dir1 will actually live in dir2. However, you can access all the files as if they are in dir1 (you can also access them directly from dir2, but we aren't going to do that here).
By installing it on the main drive (dir1), you are telling the game it is actually in dir1, and it should look at dir1 for its files. The fact they happen to be elsewhere is immaterial to the game, it's looking at dir1 for the files. Think of it like a magic portal, you step through a door and suddenly you are in neverland. The way to get to neverland is through that door.
I'm thinking this will workaround your issue as, for all intents and purposes, everything is on the main drive (they just happen to be stored elsewhere via the symlink).