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.
So this is a very general answer since it really depends on the game in question, and how you two are using the PC. Let's take the following games as just an example:
Minecraft: Depending on if you use the original launcher (minecraft.exe) or the compiled installer, each user would be installing the game once per Microsoft Windows profile. So C:\Users\Player1\Appdata\Local.minecraft counts as a single install, if it's the same windows account, but different Minecraft login, it just adds an additional file.
Team Fortress 2: Since TF2 can only be played on Steam, we're going to have to deal with 1.5 installs of this game. The first install will add the game's shared contents (C:\Program Files (x86)\Steam\SteamApps\common\Team Fortress 2) which any Windows profile can access. The second install (inside of Steam browser) will create a separate package per Steam user that logs in. This is so that your settings/downloads for TF2 won't overwrite any of your brother's settings. (assuming each person has their own Steam account.)
League of Legends: The game itself uses a launcher (much like Minecraft) but doesn't have much else to install besides the base content. In this case, you only have a single install (C:\Riot Games\League of Legends) that's shared with all Windows Profiles on that PC. You use your own login to access your account, but nearly everything is saved on the server side, allowing for only asists to be installed once.
As such, it's very VERY unlikely to find a game that will need a double/triple install. Steam does have some issues in how some developers upload their games. (ie, what's shared and what's per user) but you'll thankfully be hard pressed to find a game having to install a 30+GB game twice over for two users.