Note that New York City also has a some additional protections that are not present state-wide[0]. I'm not sure if any of those come into play here.
[0] For example, discrimination against gender identity is protected in NYC and Long Island, but not state-wide. IIRC New York also protected against discrimination for sexual orientation before SONDA (state-wide law) was passed.
Generally, New York is 'at-will', though it depends on the circumstances of employment: http://www.ag.ny.gov/labor/can-you-be-fired
Note that New York City also has a some additional protections that are not present state-wide[0]. I'm not sure if any of those come into play here.
[0] For example, discrimination against gender identity is protected in NYC and Long Island, but not state-wide. IIRC New York also protected against discrimination for sexual orientation before SONDA (state-wide law) was passed.