When James Damore, a Google engineer, was fired this week for writing a 10-page manifesto spelling out his grievances with the company’s progressive values and positing that biological differences explained the tech industry’s gender gap, it might have seemed like the end of a bizarre, short-lived morality tale.

But for the alt-right, the battle was just beginning.

Minutes after Mr. Damore’s firing was announced, a flurry of right-wing websites, message boards and social media cliques sprang into action, eager to paint the episode as another example of liberal political correctness run amok. A headline on Breitbart, the conservative news site, screamed in capital letters about “blacklists.” Users on Twitter and 4chan, the message board beloved by pro-Trump types, began to organize a boycott of Google’s services. Milo Yiannopoulos, the alt-right provocateur, called Mr. Damore’s firing “disgusting” in a Facebook post, and offered to help him land on his feet.

For alt-right activists, who occupy the rightmost flanks of a powerful conservative internet subculture, Google’s response to Mr. Damore’s memo was low-hanging fruit for mockery. But there is another reason that the alt-right’s opposition campaign appeared so quickly, with such well-practiced maneuvers.

For the last several months, far-right activists have mounted an aggressive political campaign against some of Silicon Valley’s biggest players. Extending their attacks beyond social networks like Facebook and Twitter, tech’s typical free-speech battlegrounds, they have accused a long list of companies, including Airbnb, PayPal and Patreon, of censoring right-wing views, and have pledged to expose Silicon Valley for what they say is a pervasive, industrywide liberal bias.