The standard COVID tests in New York seem to take 5 days for results, which isn't enough for Canada's requirement that you have a negative test within 3 days of your flight into Canada. Luckily New York also has rapid testing, which will gives same-day results. However, I'm not sure if those tests are one of the accepted molecular tests for travel to Canada.
The New York state webpage you cite in your question contains this:
All tests performed at these sites are PCR-based laboratory diagnostic tests
The Canada webpage you cite in your question contains this:
Types of Accepted Molecular tests
These test methods are considered acceptable molecular tests:
PCR - Polymerase chain reaction
So the answer is "yes," the New York Rapid Test qualifies under the Canadian rule.