Hi @r-c thank you for your post here on the Zoom Community! This is a very unusual situation and we have seen sometimes that the registration link has been sent and has been slightly modified in transit somehow. This results in the registration page showing for someone, like you are seeing, but the "register" button at the bottom of the form is not clickable.
It would be great if you could report back to the meeting organizer and see if they can send you the link in another way just to see if that fixes the issue. For the meeting host, they can sign into the Zoom portal and view their meeting by clicking on it (not editing, but actually clicking on the meeting name)

If they scroll down just a little bit they will see the "Registration Link" and they can right click that, copy it, and then send to you. They can also click on the far right where it says

Then copy that and send to you. If you could have them try that and see if it works that would be much appreciated. Maybe you and the host can even compare the link they send this way to the link you received in another fashion and see the differences?
If this has answered your question to your satisfaction, please click the "Accept as Solution" button below but if not please reply and we can continue the discussion. Thank you!