As a verb, it's used the same as Merriam Webster defines it. There is no need for it to be the government, just someone that is suppressing or deleting things that are objectionable.
Everyone knows what is meant here, so there's no problem with the clarity of communication.
Finally, you're making assumptions. I'll leave it at that.
I agree, it just happens that your narrative is wrong.
There are important distinction to be made between government and private censorship, of course. Nevertheless, the word "censorship" never implies "government censorship".
Censorship laws do not protect against this type of "censorship". So yes, out of context it meets the vanilla definition of the word. Unfortunately, in the current sociopolitical environment where such things are front and center, the word is misleading.
Spotify is not Uncle Sam, and vice versa. Context matters, and therefore censor is an extremely poor choice. It hurts more than it helps. In fact, it's close to clickbait.
Many TV stations literally have censorship departments, whose job it is to decide what is and isn't shown, in line with the agenda of the network, not merely what the law mandates.
Therefore, it's the wrong word. Cencorship laws do not protect this type of "censorship". Now people get confused. And so on.
At best, this is self-sensorship. JRE, at will, entered into a contract. JRE was well aware some shows would not migrate.
It's clickbait. The headline should read: ".Spotify Declines to Migrate Some JRE YouTube Content." Full stop.
Your original claim is what I care about: "This is not censorship" is what you said (paraphrased). That's wrong. It's a misconception.
Why is that important? Because we should be worried about corporate censorship as well, not just government censorship. In fact, right now, the government is censoring almost nothing, but corporations are using censorship to maintain "good" ideas and narratives in the heads of their viewers while keeping out the "bad" ones. There is no space for "dissident" or "heterodox" views, neither on left-leaning nor right-leaning media. It's polarizing the country. I don't think that's their job.