Hi Cameron,
Thanks for reaching out.
You mention buying a personal license for your client; in your account records, I see that you only bought a license for Events Calendar Pro.
In your screenshot, however, you are trying to enter this Events Calendar Pro license into the field for the Events Aggregator product.
Events Aggregator is not Events Calendar Pro so this error will persist!
Make sure you install and activate Events Calendar Pro alongside The Events Calendar; both plugins need to be installed and activated on your site! (Head here for file downloads of Events Calendar Pro and anything else you buy → http://theeventscalendar.com/my-account/downloads)
Once both are activated on your site, use the steps here to activate your license → https://theeventscalendar.com/knowledgebase/finding-and-inputting-your-license-key/
Cheers! 😀
George