Hi,
I just tested installing the app, and it worked fine on my end even with Snipping Tool minimized on the taskbar. The app does seem a bit outdated since its last supported OS was Windows 7, so it's possible you might run into some issues like being unable to override the PrtSc key. That said, you could try uninstalling Snipping Tool to see if that helps. After removing it, restart your PC, then uninstall and reinstall the PrintKey app.