Use Steam/Proton (a.k.a. Wine) on Linux to run Windows games which are not part of Steam?

I am using Steam on Linux and am very happy. I have purchased many Windows-Only games on Steam which play flawlessly on Linux/Steam with Steam's Wine-implementation called Proton.
Now I would like to "import" Steam-external games like Starcraft2 and run them with the help of Proton.
Can I somehow do that - or do I need to install a separate copy of Wine?
Best Answer
I found an interesting reply on Proton's github. Apparently there is a way to run non-steam games with just the Steam client.
Do these steps once:
- Go to your Steam settings, "Steam Play" on the left and Enable Steam Play. Optionally, Enable it for all titles too, so that you need fewer steps for each game you want to add (though I suggest against it, see below).
- After Steam restarts go to the "Tools" section of your Library and install any Proton versions you are going to use. If you don't know, select the most recent one (currently Proton 4.2-2 is the latest).
For each game:
Go to Steam's main window, on the left-down corner click "Add a Non-Steam Game...", "Browse...", change the File type to "All Files", find your game's Windows executable and add it to your library.
(Optional) Right-click the new entry, go to its Properties, name it as you please in the first field and select "Force the use of a specific Steam Play compatibility tool".
Note that if you didn't choose to Enable Steam Play for all titles in the settings, this step if REQUIRED otherwise it's going to run using your system's wine version.
Even if you selected that, you may want to try different versions for each game and see what works better. Remember to have the corresponding Proton version installed from Tools, otherwise, it falls back to system wine again.
Launch and enjoy.
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Can you play Windows Steam games on Linux?
That said, there are plenty of Steam games that will run on Linux, and quite often, a Windows Steam game can be convinced to run on Linux even though some 'fettling' by the user may be required. This approach is officially supported by Steam using a system called Proton.How do I play a Proton Game on Steam Linux?
Can I Install Non-Steam Games Using Proton? The short answer is, yes, you can. The Steam app allows you to add Non-Steam games to the Library.Can Steam Proton be used for non-Steam games?
You can download the ....Add it to Steam.How to Fix Windows Games That Are Not Working with Steam Proton - Three Possible Solutions - Linux
More answers regarding use Steam/Proton (a.k.a. Wine) on Linux to run Windows games which are not part of Steam?
Answer 2
If you look on the wine official website, you will find that Starcraft II is supported out of the box with Wine. This means that all you have to do (in theory) is install Wine, then install StarCraft II, and it should work without any playing around with the configuration.
Sources: Stack Exchange - This article follows the attribution requirements of Stack Exchange and is licensed under CC BY-SA 3.0.
Images: Laker, Andrea Piacquadio, E M, ready made