The hypocrisy of the NYT as an institution does not invalidate their points about Google. However, their points about Google do not make their own practices any better.
It is also true that individual journalists and opinion authors don't get to decide how the NYT operates. However, they do get to choose what they write about -- and by broadly emphasizing Google's policies and by broadly ignoring the policies of institutions like the NYT, journalists risk rephrasing the cultural debate over privacy as "normal people vs big tech" rather than, "normal people vs big tech, the government, publishers, and the entire ad industry".
Journalists do not have a responsibility to force their publishers to change, nor is it a problem for them to write articles that focus on Google. However, journalists do have a responsibility to research and understand the broader topics they are reporting on -- and it is not incorrect for readers to observe that we're seeing a trend of journalists who are remarkably hesitant to apply the same level of reporting scrutiny toward publishers and news organizations that they do towards other institutions.
It's also not black-and-white whether this criticism is counter-productive. To the extent that it shelters companies like Google and plays into "whataboutism" -- yes, it's a problem.
However, criticism of this nature is also the reason why NYT as a publisher has recently started to get more self-aware of their own practices. If journalists see criticism of this nature and it makes them more likely to report on publisher privacy policies, that's productive. If institutions like the NYT get criticized and it leads to them internally examining and changing some of their own privacy policies, that's very productive.