This says "Schmidt, she said, was threatening to pull his name and substantial funding from New America in retaliation", but previous articles have said that Schmidt simply mentioned his displeasure and Slaughter took care of the rest.
I'm not exonerating Google here regardless; calling the head of a think tank (as opposed to, say, the essay writer) to express displeasure is obviously a display of power. But it's interesting as a taste of how authoritarian behavior works.
Schmidt couldn't have ordered the article spiked, and he would have looked terrible if he expressly said "I'm pulling funding if you criticize Google". So instead, he calls and says "I'm unhappy about this article". And Slaughter, not being an idiot, recognizes that she got the call for a reason and needs to act. If she hadn't been so blunt about her internal message, everyone could have quietly insisted the firing was "for other reasons" and left the whole point unproved.
In one sense, the news story here is that an explicit message was sent. A sensible person ought to expect that soft power and unstated implications cause similar consequences every day.