Taken literally, the answer to your question is obviously YES.
The companies obviously applied censorship, and the nature of that, which was censored, was political. The term "censorship" in disjunction from government is however a rather neutral term, as others have pointed out.
The spirit of the question seems to be whether the censorship in this case was problematic or not.
Making a judgement focussed solely on this particular case would be opinionating, which isn't allowed, and obviously at this point pure speculation.
It is therefore much more helpful for this question to point out that the general state of the big tech companies is currently "problematic".
The comments already mentioned Section 230, which at his core states:
No provider or user of an interactive computer service shall be
treated as the publisher or speaker of any information provided by
another information content provider.
Section 230 furthermore grants those providers the right to apply moderation to their service, as long as they do it "in good faith".
The vagueness and shortness of this law make its age quite unsurprising: Its from 1996.
In 2020 however we are facing huge tech companies that effectively hold monopolies in their respective business sector. There is only one Twitter. The alternatives are neglectably unimportant.
With regard to those monopoly-holding giant corporations the term "in good faith" becomes a big issue since the way in which those companies apply their guaranteed right of moderation has potentially wide reaching consequences.
Let's take the current issue that triggered the question:
It doesn't matter whether the NYP story was 100 % true, 100 % fake or something in between, or whether the actions of the tech companies were factually/morally right or wrong. What this whole affair shows once again is that these tech companies have a ridiculous amount of power under current law, potentially even the power to swing elections.
When they decide to censor something, this censorship, owing to their monoply, effectively carries the same weight and power as government censorship, which is a problem, regardless of whether it was justified in the underlying case.
In one way or another this issue will have to be adressed. After the current event maybe sooner than later.
The currently most commonly discussed possible measure is treating and regulating social media as a public utility.