I don’t think that’s the argument they’re making. I think they would concede that Google has a property right, and may at it’s discretion moderate content. However, they would argue that Google shouldn’t exercise that right because it is harmful to the culture of free speech. This is volunteerism, which is to say they should choose to hold themselves to a standard without being forced to do so.

I’m not sure how I feel about it, but I think I’ve summarized the best version of the argument.