After some rereading and a consultation with an authority on NY State Real Property Tax Law, I have learned that the MTA does not pay property taxes on their tracks or on stations or other property they own, however it is listed on the tax map but only for use as a point of reference.
The US Postal Service does not pay property taxes in NY on any property they own outright. However, the federal government and its agencies and assigns do pay property taxes on properties they lease. Thus, most likely Amtrak does not pay property taxes to NYC for the NEC, Sunnyside Yard, or Penn Station.
Private railroads do however pay taxes on their property in NY so CSX, NS and CN would pay taxes on whatever property they own in NY. Sorry for the confusion.