EDIT:

Controller didn't work under linux, solved the problem.

For controller support to work in linux you may need to add this game to your steam library and start it from there. No need to buy it at steam, just add it as a non-steam game and start it from the steam interface.

I have an Dualshock4-Controller with ds4drv via Bluetooth.
I had no issues using my controller.

I tested the gamecontrollerdb.txt file on Debian Stretch and have not been able to get my SF30 Pro controller to work at all. Here's what I did.

I copied the file to /home/My_user/GOG Games/Owlboy/game originally. Nothing happened. Then I tried moving it to /home/My_user/GOG Games/Owlboy, still nothing happened.

I decided to inspect the file and found out that the line for a specific controller seems to be exactly the same for all OS sections, except the very end where it says the platform ("Windows", "Mac OS" or "Linux"). Since my controller only appeared in the Windows section and the line appears to be the same for every OS, I copied the lines for my controller from the Windows section, pasted them in the Linux section, and changed the "platform:Windows" to "platform:Linux." That didn't work, either.

I have had issues opening Windows-created txt files in Debian. It complains about UTF-8 or ISO-8859-14, which seem to be file format coding standards. I hope adding the two lines in Linux hasn't caused the file to change format, preventing the game from recognizing it.

After modifying the file, I retested it in /home/My_user/GOG Games/Owlboy/game , then in /home/My_user/GOG Games/Owlboy. Still no luck getting the controller recognized by the game.

The controller itself is not an issue since it works 100% with all other games and emulators, both wired and wireless. I don't want to buy a Dualshock 4 just to get this game to work with a controller, but I'm running out of options. Anyone have any other ideas?

I guess no one is even looking at this forum. If anyone ever sees this, the game recognized my wired Dualshock 3 I dug out of a box somewhere and it works 100%.

Did you read the ArchWiki linked section? Compile the controllermap.c program (SDL source) and it will generate a mapping for the specific controller. No need to try to guess it.