Those retail discs were created prior to the sale of Impulse to Gamestop and will be installing the then-current version of the app, which may no longer work.
Do I no need to register an account with Stardock just to play the game now?
Yes, a Stardock account is required to register and play the games if you have downloaded them or obtained updates online (the initial retail version should not). It will be the same account you're using to post on the forums though, so you already have that part done.
As Impulse is no longer owned by Stardock, the account systems are separate. But as Sins Trinity and GC2 Ultimate are now available from the Stardock store for direct download once you have registered them with us, you need not bother with Impulse/Gamestop at all. You can download the entire latest version of those games straight from us in your web browser (patching capability is forthcoming with the new SDC app's release).