The delay appears to be due to both ATC AND crew (likely an ATC delay somewhere in the network preventing the inbound crew from reaching MCO, as the aircraft seemingly arrived inbound on-time, according to AA.com). I'd guess AA could interpret that in their own favor if they wished. Fortunately, seems like they did the right thing here.

Their responsibility depends in part on the reason for the delay. In this case, they seem to have taken liberty to provide a hotel (and I'm guess meals) for the party traveling. Looks like the next flight out is tomorrow from JFK on EY at 3:25PM, they'll arrive about a day late. There appears to be plenty of space on that flight. If they've been rebooked to the 10:40PM flight tomorrow night, double check to see if the earlier is available. It's on a Jet Airways-operated aircraft, BTW.