The email she posted [1] makes it pretty clear that she sent an email with some demands/conditions (separate from the one "to Brain women and allies") and said that she would resign if they weren't met. Google said they wouldn't agree to them, accepted her threatened resignation, and told her it was effective immediately. Without knowing more context, it sounds like she tried to do some hardball negotiating by threat…
There is still a civil way to accept a resignation, with proper timelines and transfer of responsibilities. She offered to resign in some time due to some demands, and the immediate termination seems to be related to an email unrelated to those demands. This sounds a lot like a sleazy move by Google to couch an immediate firing as a resignation.
It's also pretty common in roles like sales and PR to be shown the door the day you give notice, especially if you're going to a competitor.