Legality of passing on the right is situation dependent, as noted by your own link:

http://www.nysdmv.com/dmanual/chapter06-manual.htm

"Before you pass on the right on multilane roads such as expressways, make sure you check your mirrors, use the proper signals for lane change, and look over your right shoulder for other vehicles. After passing, be sure to check over your left shoulder, and to signal, before returning to the left lane."