To give a bit more detail here: In Desktop Mode, you can access the normal PC interface of Steam. There’s a Menu Entry in the “Games” Menu that’s titled “Add Non-Steam Game to Library”.

This is what you need. It opens a list of applications that are in the menu (to be precise: for which a desktop file exists in the appropriate folder), but you can just click the “Browse” button. After clicking that button, change the file type filter to list all files, and find the game’s executable. If it’s a Windows game (or a really old Linux game) you’ll need to go to the game’s properties in Steam and force a specific compatibility tool. For Windows games usually a recent version of Proton, for really old Linux games the “Steam Linux Runtime”.

That’s it.

In order to copy the games’ files to the Steam Deck, I usually install the game on the desktop first, and then just copy the installed files over via sftp. I’ve written a long and boring explanation on how to enable sftp on the Steam Deck here.