On my current CPU I just downloaded the GOG Galaxy client. I have the Witcher and GWENT installed on my CPU, but it doesn't show up as installed on the client. Where the games should be showing it reads, "You have no games installed yet". How can I fix this?

Other then your incorrect usage of "CPU" which is kinda of cool too
on Galaxy click the GOG.com icon (see attachment) and click scan and import folders and that should solve it.

I make no Guarantees that it will work as Galaxy seems 50/50 on that function.

Blimey, you must have a cracking CPU!

Hah yeah, that jumped out at me too.

Good to know I am not the only one :D

If Lord_Kane's suggestion doesn't work, it's also possible to manually add installed games... only I can't describe it in detail because I'm at work so don't have Galaxy to hand.

Welcome to the forum, Captain_Meemo!
Usually Galaxy should automatically detect installed games. If not detected, games can be added through following methods.
Method 1:
- open GOG Galaxy
- Click on the circular menu button on the top of left hand side panel
- Click on Scan and Import Folders option
- Click on Select Folder
- Browse the folders where the games are installed
- they should be detected and appear on the left hand side panel

Method 2: If Method 1 doesn't work
- Open Galaxy
- Click on Library button in the top menubar
- This will open your library (attached to your GOG account)
- Click on the game you want to add
- This will open a game page
- Click on the More button
- In the small menu that opens, hover your mouse cursor on Manage Installation
- In the new menubar that opens click on Import Folder option
- Now browse the location where the game is installed and Galaxy should detect the already installed game and add it to its list on the left hand side panel

Hope it helps
:)
Have a nice day!! Done
:)

Excellent!