Corporations have the ability to take things away and this can definitely affect individuals and groups in major ways.
However, the difference is that corporations are, at least in theory, opt-in. If you don't want to use Google or pay for someone else's product, then you don't. The government not only makes you pay for it's programs, but it puts guns in your face if you are willing to accept the hardships of not using government services. That's why censorship and other governmental actions that undermine individual rights are a special problem with special restrictions. I am happy to be an American, but if I wasn't, I'd still have to deal with the US government or some government no matter where I go or what I do.
It may be difficult to create a viable competitor to a multinational, but it's not illegal to try and it does occasionally happen. That's the distinction. If you want to have a content search engine that brings up content that Google won't, you (may) have a means of providing value that Google isn't. That means that you can more effectively overcome Google's absolute mastery of capacity and search algorithms because your audience cannot use Google for what they want.
Of course, you might find that the problems and risks inherent in allowing unfettered search on all content isn't justified by the small amount of reward. And this is likely Google's calculation as well. They probably get fuckall, comparatively, for ads based on "adult" search, while at the same time, they need to be wary of liability or moral outrage for hosting the results for those marginal sites.
This is not the same thing as government censorship, although the root causes can be similar. Corporations must shift for themselves, and like an actual person, they're going to have their own risk to reward ratio. Not everyone feels like being jailed or tear gassed for their principles, and Google is probably becoming similarly risk adverse, but does that surprise anyone really? They're a public company and have been for years now.
Is what Google doing "censorship"? I suppose, but if we accept the use of that word to describe what Google is doing, we still have to make a distinction about what is really going on. Would you like to be forced to accept risk for something you don't really believe in? Probably not, and certainly without some sort of protection against those who would have a problem with you.