Yes, it works on M1. All of the training videos were done on M1 and a bunch of users are using M1 too. No issues have been reported at all on M1.
Make sure your Creative Cloud app and Photoshop are both up to date. If the installer still won’t run then you may need to uninstall and reinstall the Creative Cloud app…. not just Photoshop…. the entire Creative cloud app because that handles the installers. However, try updating Creative Cloud before reinstalling.