You should need to verify the email address for all new accounts by default. From the screenshot, it looks like an email was sent (“last emailed” - 1 day).
You can activate their account manually from their user admin page if you are confident they’re not a spammer, but it would be better to find out exactly why they didn’t receive the email so that they can then receive email notifications, digests and password resets etc.
You can check your sent email logs by going to [YourSite]/admin/email/sent, and you can even filter them by username or type (eg. ‘signup’) to help narrow them down. 
I’ll add the obvious, just in case, but it’s worth getting the user to check their spam folder. 