I find it hard to believe that Google would build a custom Chrome extension for this - they already own Google Calendar and all of the data in employee’s calendars.
Google owns Calendar... but Calendar is written by their employees, the very people they're trying to control. Using a separate browser extension means a small team can manage this code and it isn't affected by larger teams' access to the project.
So why bother with an extension then?
As you point out, they own Calendar, they could just add it there.
As the spokesperson says in the article, they might genuinely want to nag people who create excessive meeting invites. Perhaps someone thought there was no need to bake this into the Calendar application.