I just tried running it on Linux and ran into the same error.
As the above conversation hinted, even though Moonring.exe is an exe, I'm able to treat it as a zip file and unzip it to a directory. Searching that I find no mention of firstDungeon-01.png
Looking at the files and line numbers mentioned in the above error, it looks like the code at the point of the error is trying to _create_ a file called data/save/firstDungeon-01.png. In LÖVE writes typically don't go into the directory containing the source code but a separate "save directory". On my system (and according to https://love2d.org/wiki/love.filesystem), the save directory is at ~/.local/share/love. Putting all this together, I tried creating a directory from the terminal:
mkdir ~/.local/share/love/data/save
And it seems to work! At least I'm able to get to the start of the game. I hope that helps you @berru_dev and anybody else on Linux. Feel free to ask if you run into any more issues. I love how open the devs have been with this game, and I'd be happy to give back in any small way I can.
Now, time to try it out!