Footage captures the horrific moment a nut fatally shoved a beloved 76-year-old former teacher down a flight of concrete stairs at  a Manhattan subway station. The deeply disturbing clip shows retired elderly educator  Ross Falzone walking toward the 18th Street subway station in Chelsea around 3:30 p.m. Thursday when his attacker walks up behind him without warning and pushes  him with both hands — sending the helpless victim plummeting to his death. Rhamell Burke, 32, smiles as he’s arraigned Saturday for the attack. Michael Nagle for NY Post The flailing victim  disappears into the lights at the bottom of the stairs — and was later pronounced dead at Bellevue Hospital after suffering a severe head injury. After the attack, his accused  killer is seen casually walking away and even signals traffic to stop as he crosses the street and disappears into the night. The harrowing shove was caught on surveillance video obtained by The Post.…