Not picking a side is not allowing political discussion, no matter who you (or they) perceive to be right. Coincidentally, this is also the choice that makes most sense to a corporation which stands to lose a lot from picking a side. Players will likely respond to sensationalist reporting of this case, but forget about it soon after, while the Chinese government is not gonna go easy on Blizzard picking the other side.
But nearly every large company in America engages in political discussion when they talk about diversity, feminism, and inclusion. I think that's a good thing, but it's clearly not the case that these companies shy away from making progressive statements.
All they are doing is saying things which a certain audience wants to hear. Nobody really cares about inclusion or diversity. They just claim to do so, because in this day and age, they will benefit from doing so.
It doesn't cost large companies any money to make feel-good progressive political statements on social media.
However when it conflicts with their pocketbook, they stay quiet or internally oppose them (example: Zuckerberg trashing Warren for antitrust and privacy issues).
In other words they do pick a side - they side with Chinese government, because the communist party has a leverage on them.
But we have a leverage too!
If we manage to damage their brand and profit, they may decide that censorship is not to their benefit.
We need to be loud and clear - communism will not be tolerated. Otherwise, it will start to creep trough Blizzard and many other companies, and limit our freedoms too.
