It's not an upgrade because there's no old version on the new OS. You might try installing an older version and see if the works then. But I'm afraid you'll need to pay for a new license if you want to have 2 copies on 2 different OS'es.

What happens if you run the Vista program from your Windows 7 OS? Just browse to it in Windows Explorer or Computer and doubleclick. I expect an error, but it's an interesting experiment nonetheless.