On the game's store page, it has the penguin icon for Linux, lists Linux system requirements under the game description, however, it lacks Linux on the 'Works on' field on the right. When in check out, it states, "1 game from your order is NOT compatible with your Linux". So does this have a native Linux port on GOG or not?

The game works fine on my Arch using KDE. On the download page you have choice between Windows, Mac and Linux, with Android version in "Extras". GoG can be a bit silly with Linux support when you are not using Ubuntu, so that might be why you saw this message