As someone who was against the backlash against Damore memo, I am also against the firing or quitting of Pichai. We should hold the company responsible for this, not the current CEO, that may, or may not have been pushed to fire Damore or react in the manner that he did. If anything, the point should be to change the management attitude and not replace it until we are satisfied with the person managing the company.
As for Damore getting fired: Google had no choice after the memo was leaked and became viral. Firing him might bring the ire of the freedom of speech crowd but not firing him might show them to be in support of an anti-diversity stance and corporations today can’t allow themselves to have that stance, which will probably lead to multiple lawsuits.
I don’t imagine that Damore will have any problem finding a job. He’ll probably get a much better deal than the one he got at Google.