Scott,
I looked at your website and you have the Crowd-Sourced Blacklist enabled. This means you may not have received the emails because other clubs have blocked (via their blacklist) the emails Zoom sent. (like Brian is pointing to)
Here is how I have told people to set this sort of thing up in the past--it has worked for them:
1) Disable Crowd-Source Blacklist temporarily (in Email and Contact Forms module)
2) If you are trying to set up the external service with an officer email that is not yours, then *temporarily* change it by setting yourself as that officer in Membership Management. (Make sure to save the change.) This ensures that you get the emails from the service to approve the registration. (Tell the officer you are doing this.)
3) Set the officer email in the Zoom website. Note that most services are set up so that anytime you would change the email address there, it would trigger an approval email sent to that new email address. (Be aware of this.)
4) Go back to your email to find the approval email... (sometimes this is not immediate depending on server loading...give it up to 30 mins)
5) Click the link to approve the new email.
6) Log out of the Zoom website then log back in to verify that the change "took".
7) Assuming change was made, then we need to undo the temporary changes made to enable this to work...
8 ) Go back into Membership Management and set the officer back to the correct person.
9) Determine what the sending email address was for the approval email, and put it (or the domain) into your clubs email whitelist. This will ensure you get emails from the service even when you are using the crowd-sourced blacklist feature.
10) Re-enable crowd-sourced blacklist.