My wife and I just to moved to CNY on military orders. She works from home for the same company out of Texas that she did before we moved, so should she have to pay the SDI tax?

Yes, because she is considered to be employed in CNY, even if the company is in Texas.

Just to clarify I assume that "CNY" means New York City (usually written as "NYC," not "CNY"). I agree with AtlantaTaxExpert - you pay SDI (state unemployment or disability insurance) to the state where you physically are present for work. This is because if she is let go from the job she would be eligible to collect NY State unemployment benefits. Her employer should also be withholding NY State and NY City income tax - are they?