Help with calendar sync

Here's what I know - Outlook for Mac 2016 synchs calendar events with only Outlook Cloud Services (Outlook.com), Exchange, and Office 365 accounts. Outlook has a "On My Computer" calendar (which you know). OS X has a sync service that connects to the accounts it has been given proper credentials and it runs in the background (which you likely know). When you have accepted an invitation (as you have described) it is scheduled in your Gmail account and coordinated with your macOS Calendar app; Google and Calendar will push the calendar event to connected devices.

I don't use Outlook for Mac often due to its limitations, but I test it out for my company regularly - one of the limitations of this app is the calendaring that you have issues with - email, notes, contacts all work as expected. My Outlook app of choice is Outlook for Windows 2016, but that doesn't help you here.

Outlook adds/schedules the Google Calendar event in the "On My Computer" calendar because of the linked invite, not because it's synched to Google's servers as you have indicated - Outlook doesn't sync to Google Calendar accounts, rather, it will add events included in URLs and store them locally (On My Computer).

Outlook does not (yet?) sync locally as Entourage 2004/8 did. Recognize that the accepted invites are not "synching" to Outlook 2016 but rather being added to your local account - changes to those accepted events would only be synched back via the embedded URL and not via CalDAV actions.

The only "workaround" I can think of is to create an Outlook.com account and connect it to your Gmail account, then use the Outlook.com account to manage synched data. One can also send Gmail events via Outlook.com, using a Gmail account as the source account. Cheers.