Do I have to reinstall a game for multiple accounts?

I have kinda an odd question. Me and my brother sometimes share a PC and we both have different accounts. So let's say I have Rainbow Six Siege on my on my account and I download it off of my account. Would he then be able to just use that same download on his account as long as he owns the game, or do we have too have two 40 or so GBs of the same games on this pc? I apologize if that is a little confusing but I could not find anything about this on Google.

As to my current knowledge, uPlay Terms of Service does not allow technically common library for separate accounts, so separate download will be necessary for each account. If someone around you is really confident with PC scripts, he may be able to do some tricks, but without real experience I do not suggest that.

In case of Steam, you can set Family sharing, where you need to specify other steam accounts, which if logs in on the PC, where the game is installed, the "shared to" user can also play the game. It is not per game basis, but installed game by sharer account. The game mentioned as example (Rainbow Six Siege) is available on Steam. In many cases CD-keys (even if it was not on CD) work on Steam too. It worths a try.