Swarm Queen is only tested for Windows, and I don't know if it's possible for it to work on Linux. (On the store page it's listed for Windows-only)
Adobe Air shouldn't need to be downloaded, as it's packaged with the game (if you go "Manage" --> "Browse local game files", you should see "AdobeAIRInstaller.exe")
It can also be downloaded from the company that maintains it (https://airsdk.harman.com/runtime), however I notice there's only a Windows/Mac option.

If it doesn't work, feel free to use Steam's return feature. There should be an option for "didn't work on my system" or something like that.

I already played the game on Windows and really enjoyed it, so there is no way I'm returning it, but you said the Installer.exe already has everything it needs in the game files?
I already tried the link you recommended and found only 2 available Runtime version of Adobe AIR.
Both of them didn't work when put into the same folder as the Installer.

I'm starting to get desperate. Can I ask you to port the game to Linux? Or would that be too much to ask?
It's just that no matter what I do, that stupid installer just doesn't want to work.
I still have Windows Emulators as a last resort, but they have either very bad performance or a very annoying/complicated installing process and I would kinda like to find a way that other potential players can easily replicate.

Can you tell me which Adobe AIR version the game uses?

Unfortunately, as far as I know, the game is Windows-only. It's not possible to simply "port" to Linux, and it uses Adobe AIR which seems to be Windows/Mac only.

I don't recall which version of AIR is bundled with the game, but it doesn't have to be in the same folder as the installer; you need to run the exe to install Adobe AIR. However if the version in the folder or the latest version won't install, I think that means you're out of luck for Linux, unless anyone else got it working somehow. :(

Yeah, I didn't really expect you to basically rewrite the game, but I thought I should at least ask.
I got a friend to help me install a virtual machine btw.