This is not about free speech. Some might argue that the game would fall under free speech and the government could not forbid it for existing. And that would be true, but besides the point. Although some do argue that the game itself should be forbidden, since it leads to imitation, but that has been disproven for games, including adult games.
So the haters have no legal grounds either way to call for bans of the game. And resort to bullying platforms, credit card companies and riling up an angry mob in social media to effectively ban it anyway.
And they did not use "free speech" for that, but lies and harassment. Platforms and eventually the developers rather removed the game, than deal with that pressure.
It is not in dispute that a platform can remove any kind of content for any kind of reason.
But it should also not be in dispute that harassment is not ok to achieve such goals. And that it is also not ok to gather supporters by using fallacies and outright lies. Unfortunately, a lot of people justify the means by the ends, since it hit a nieche game they in particular would find disgusting anyway.