Thinking that Baidu banning photos of the Tiananmen Square protests is not the Chinese administration exercising its power, because the banning itself is done by a private company? Yeah, that would be comedy stuff.
In China as in the U.S., these are not local mom-and-pop stores exercising their rights to free association. These are large tech companies and business ventures that are deeply and inseparably intertwined with the state and the political parties (both of them), based on the granting of reciprocated privileges. They know full well that if they ban the wrong person (or refuse to ban the right person), they face being regulated out of existence the next day: indeed, seeing this threat, they're scrambling to align themselves with the incoming administration. Yes, they had deals with the previous administration too [1].