The only way that any add-on can send more emails than the Gmail recipient quota of that account, is to use some external mail sending service.
And the add-on would need to make a UrlFetchApp.fetch(url) request to some external place.
It's not apparent what mail sending service Mailmeteor uses.
Maybe someone else knows.
I did install it and took a look at it, but didn't sign up for a plan.
I looks like the free Mailmeteor plan just uses the Gmail quota of the account that installed the add-on.
I'm assuming that once you pay for a plan, that the add-on makes an external request with UrlFetchApp.fetch(url) to the external mail sending service.
Mailmeteor does ask for permission to send emails from your account, and to make external requests.
It's possible that Mailmeteor has it's own mail sending service, and uses the Google add-on as a way to reach customers.
But I'm just guessing. Send Grids lowest plan is $15 a month, and Mailmeteor's cheapest plan is 8.99 a month.
So Mailmeteor would be loosing money unless they had a plan that cost them on average less than 8.99 a month for the same number of emails sent.
It's an interesting question.
I don't have the real answer, but those are my thoughts.