Have you spent time with the program?
What / Where does the program read/write to or from?

What could it possible do that requires "domain" admin to run..??

I have seen a few software packages that use local admin to cause less problems for
lazy admins.

What platform are you running?

Does something run as a service?

Does it write to AD or system files?

Its just so hard to see a vendor selling such nonsense...