Can I file state taxes for two states (MA,NY), claiming to be a non-resident at both?

New York uses the concept of domicile in relation to whether or not you are considered a tax resident of the state. From the New York State FAQ page you linked to:

How do I know if I am a resident of New York State for income tax purposes?

Generally, you are considered a New York State resident for income tax purposes if you are domiciled in the state. For most people this is straightforward: the primary residence where you live is both your state of domicile and the state in which you are a resident for tax purposes. However, you can still be considered a resident of New York State for income tax purposes even if you are not domiciled in the state. (See below, “Can I be a resident of New York State if my domicile is elsewhere?”)

Can I be a resident of New York State if my domicile is elsewhere?

You may be subject to tax as a resident even if your domicile is not New York.

You are a New York State resident if your domicile is New York State OR:

• you maintain a permanent place of abode in New York State for substantially all of the taxable year; and
• you spend 184 days or more in New York State during the taxable year. Any part of a day is a day for this purpose, and you do not need to be present at the permanent place of abode for the day to count as a day in New York.

As you can see, the "184 days" requirement does not apply if your domicile is in New York.

From what I can tell from your question, it sounds to me like your domicile is now in New York State. If I'm reading this correctly, that makes you a New York State resident, regardless of the number of days you have been there.

As for Massachusetts, their page states:

Full-year residents

If you're a full-year resident with an annual Massachusetts gross income of more than $8,000, you must file a Massachusetts tax return.

You are a full-year resident if:

• Your home is in Massachusetts for the entire tax year; or
• Your home is not in Massachusetts for the entire tax year but you:
• • Maintain a home in Massachusetts; and
• • Spend a total of more than 183 days of the tax year in Massachusetts, including days spent partially in Massachusetts.

Full-year residents use Form 1: Massachusetts Resident Income Tax Return.

Part-year residents

If you're a part-year resident with an annual Massachusetts gross income of more than $8,000, you must file a Massachusetts tax return.

You are an individual part-year resident if you:

• Move to Massachusetts during the tax year and become a resident; or
• Move out of Massachusetts during the tax year and end your status as a resident.

Part-year residents use Form 1-NR/PY: Massachusetts Nonresident/Part-Year Tax Return.

The "183 days" requirement does not seem to apply to you, either, because you no longer "maintain a home in Massachusetts.” Instead, you seem to be a part-time resident, because you did "move out of Massachusetts during the tax year and end your status as a resident."