The edit equipment button on your profile page might be trying to open the game window to allow you to edit your equipment in the app.
I guess the easiest solution is just to open the game directly and do the editing there.
If you really want the edit equipment button to open the game, you could try downloading and installing the latest version of the game. There's no need to uninstall the game first as you only need the updated launcher.
Versions of the WGT Launcher prior to 2021 I think, weren't configured to open the game using the WGT handler in your browser, so clicking on things like the edit equipment and play now buttons won't open the game if you installed it from an older version of the launcher. Your game may be up to date, but if the launcher isn't, then that might be causing the issue you're having.