Some official in the video said it was ENGINE FAILURE. / Mechanical failure.  You'd think that a siren would have blasted to warn the unfortunate sailors.  Must be a strong current at that bridge.  Déjâ vu! Any way, there are hundreds of eye witnesses... "Aye aye, sir !"
Pray for the dead.

They’re saying the engine cut out and the current pushed the ship towards the eastern bank. A ship of that height must stay mid-channel and pass beneath the highest span of the bridge.   
Yes, the currents are VERY strong in both the East and Hudson Rivers surrounding Manhattan. The Hudson flows North to South, but at the base, the Ocean tides alternately pull out and push up on the current. The northernmost and narrowest section between the Bronx and Manhattan known as the Harlem River, is extremely dangerous. Foolhardy people who try to swim in waters often drown. Amateurs who try canoeing, rowing, or kayaking have been swept out to sea, caught in whirlpools, and violently slammed against rocks, docks, and pilings. Others have gotten stranded on some of the smaller islands mid-channel and needed rescue. My guess is that the Mexican Navy just didn’t know the river very well.