Im currently live here in Dallas Texas for past 2 yrs, and im selling my house in New York, Do I need to file for IT-2663? Does Section 121 applies to me?

Q. Do I need to file form IT-2663?

A. No, if you qualify for the home sale exclusion. NY follows the federal rules for the home sale exclusion. 

Reference:  https://www.tax.ny.gov/pdf/current_forms/it/it2663i.pdf

Q. Do I need to pay for Capital Gain Tax or real estate income tax in New York State? 

A.  Probably not. Normally a non resident pays state income tax on the gain from sale of property they own in NY.  But, no in your case,  unless you don't qualify for the home sale exclusion.

Even if you qualify for the home sale exclusion (the house was your principle residence for at least 2 of the 5 years prior to the sale*), you may be subject to federal and NYS tax depending on how the house was used for the 2 years you have lived in TX.  Specifically, if you rented it out, you are subject to income tax on the depreciation recapture (even if you didn't claim depreciation). 

* If you do not meet the 2 year rule, but moved for work (or other "unforeseen circumstances"), you may still qualify for a reduced maximum exclusion.