One would think that Google Notifier for Mac would the perfect way to alert a user to requests to chat, especially requests for Google Video Chat.
One would be wrong.
Google Notifier for Mac was "Last updated August 18, 2006". Yes, roughly 50 net years ago. It's clearly one of those infamous abandoned Google hobby projects.
It provides notifications for incoming email and calendar events only. The download page documentation links display Windows Notifier documentation; you have to install it to find out what it does (once you install there is a Help menu with some content).
Scratch that one.