The situation I've explained is not system-specific and will not vary for other users on other distributions. Since a focus of the jam is guiding participants toward engaging in best practices when supporting Linux, I'd love to invite you to explore this further and gain a better understanding of why it's relevant.
Firstly, if you to use a web browser to download your game from Itch on your Zorin OS install, you can confirm what kind of experience your users are going to have (if you save it to a drive mounted that automatically gives executable permissions to all files, which I've seen some people do for drives shared with Windows, be aware that that is not a typical or default configuration).
When you tested the game on your Linux distro, it would have had those executable permissions set one way or another. If it was the system you did your AppImage packaging on, then the file would have been given those permissions when it was created. You can verify right clicking the game's AppImage file in a file browser and viewing its properties (most file browsers' properties dialogs have a permissions tab), or by running ls -la in a terminal and looking for an "x" at in the 4th column of characters representing the different permissions flags that Unix style filesystems can hold.
The key thing here is that file permissions in general are not a part of the file itself. They're stored in the filesystem - as part of the data that tells your computer how to find and read files from the hard drive. Archive formats like zip or tar let us work around by keeping some metadata on file permissions inside the archive itself that the program doing the extracting can then use as a reference when creating the extracted file. The HTTP protocol doesn't include that information, so the browser doesn't know to give it anything but whatever the default permissions are on your filesystem (which I touched on earlier, but isn't really relevant here - if you want to read up on that, a good place to start would be over here).
Hope that sheds some light!