It sounds like the beta version timed out and invited you to get the full version. If you don't have a LIcense ID and LIcense Password then you haven't shoved your money into X1's coffers.
Had you done so, they would have sent you an email with these details.
When I went to buy X1 Search 8, I also flailed around a bit trying to fathom out where to go. In the event I followed a link in the message that offered a discount for beta testers.
Hello X1 community, We cannot say thank you enough for your
You do have to login, but past customers should have the details to do that.