The official website is not working anymore, but I managed to check a cached version through Google and it appears that there is a version of PayChex available for Windows 7, but not possible to acquire it at this time.
This is what it says on the page:
Most of our products work on these standard platforms:
- Google Chrome, Firefox, and Microsoft Internet Explorer 11 and Edge on Windows 7, 8.1, and 10
- Google Chrome, Firefox, and Safari on Mac OSX 10.9 or higher