The “Dean" didn't find the NYU testing instructions “obscure" but maybe that's why I've got the fancy title. 😉 You can find the NYU test requirements here: http://www.nyu.edu/admissions/undergraduate-admissions/apply/freshmen-applicants/instructions/standardized-tests.html
You will see that NYU is (mercifully) a “test flexible" college, meaning that candidates are given a variety of test-submission options. SAT Subject Tests are NOT required by students who fulfill one of the other options. These other options are:
The SAT Reasoning Test; or
The ACT with Writing Test; or
Three AP exam scores; or
The International Baccalaureate Diploma; or
Three IB higher-level exam scores (if you are not an IB Diploma candidate)
Note that if you are submitting AP, IB, or Subject Test results instead of the SAT I or ACT, there are some rules that govern which tests you must send. Those are explained on the page cited above.
Students educated abroad may also have the option of submitting results from an approved national examination. These are listed on the Web page cited above, too.
So, if you have already taken SAT Subject Tests and are pleased with your scores on THREE of them, you can use these scores as your test-flexible choice but, otherwise, you are not expected to send Subject Tests to NYU.
Hope that ends your confusion!