How to remove bottom portion of kitchen faucet
You're looking at a nut. That ring threads onto the nipple. It may not have been installed correctly. It's intended to be used as a clamp base, with the screws you removed tightening against the upper ring. 

Partially reinstall the screws and use them to help turn the nut. Spray it with some penetrating oil or WD-40 to help loosen it. 

You could also exercise the nuclear option and cut off the old faucet above to release it from below.