My family is in Washington, but I moved to NYC in 2007 for work and rented an apartment there. I moved back to Washington in mid 2008 due to personal reasons. For my 2007 return, I filed as resident. But for the 2008 return, I filed as nonresident. NYS tax department now wants me to pay NYC tax as part-year resident.

NYS considers someone a resident if that person's domicile isn't NYS, but he/she maintains a permanent place of abode in NYS for more than 11 months and spent 184 days during the tax year. (the same definition works for NYC)

I believe my domicile has always been Washington, but in 2007, I considered myself a resident because I kept a permanent place of abode in NY for more than 11 and spent 184 days there. But for 2008, I only kept my permanent place of abode in NY for 6 months and spent less than 184 days. Thus for 2008, I should be considered a nonresident.

Does this argument makes sense? Because I don't quite understand how I can be a part-year resident under these definitions.

Thank you!

If you were present in NYC, then any income earned during that period must be reported on the NY state return.
If you lived in NYC even for a short period in 2008, you are part year resident of NY. You will report income as part year resident.
Read: Your U.S. Tax Return: Working or Living in Two or More states

But who's considered a non-resident then? Non-resident of NYC doesn't have to pay NYC tax, whereas part-year resident have to, and that's the distinction that I'm concerned about.

A non-resident is someone whose domicile is elsewhere. But you can't argue that your domicile was Washington during the first half of 2008 - having an apartment in NY, at the same time as a job in NY, means that's where your domicile was, so you were a NY resident during that time. This means you must file with NY as a part-year resident to cover the first half of 2008, as Mukata said.