It is made with the Godot Engine. If you look at Pixelorama's source code in GitHub, it's basically a Godot project. You can easily download it and run it in Godot! :)
As for your issue, we already solved it in Discord, but for anyone else that is reading, in the Web version, the only way to currently load .pxo files is to drag and drop them in Pixelorama. The "Open" option in the File menu does not work for .pxo files. This is a Web version limitation, the desktop versions do not have this issue.