I am logged in. I do see the download button. When I click it, I end up on the download for the demo.

Ok. I figured it out. I needed to apply the upgrade code from my email to my account. Now the download button goes to the alpha instead of the demo.

I just bought this, and I got a link to go to:
https://www.factorio.com/download in my email.

Yet when I go there, it says its the demo version. In the faq, there is a video link about updating. That also clicks the download button from the main page, but instead it says alpha, not demo.

So how do ...