Yeah the website isn't very clear. I think what you do is uninstall it, and then when you register your serial on the new computer it will put you through a process to deactivate the previous version. You might not even have to do that much. It might just deactivate by uninstalling it.
I've done it a couple times, and I can't even remember exactly what I did. I didn't run into any issues, though. I had to look it up to be sure, and I found this: