Yes, the New York Giants are duty bound to support disaster relief efforts during hurricanes or coastal flooding because they are a large corporation with a large public profile, and it is very important that they set a good example for the community of caring. Large corporations have corporate responsibilities to the people that comprise their customers and fans.
The New York Giants are not duty-bound to support disaster relief efforts during hurricanes and coastal flooding. I think that they have the same opportunity to donate to funds to help efforts and victims should they choose to like any other sports team. The New York Giants have a duty to just play football.
No celebrities, such as football players, should feel required to provide relief in the case of an emergency or natural disaster, just as the average citizen is not duty-bound to do so. That being said, if they live in the state that has been impacted by it, they will hopefully feel as though they should. Providing support means more when it's not something someone is forced to do.
I do not think that the New York Giants are duty bound to support disaster relief efforts, but it would be the proper thing to do to show solidarity to the fans that help make their careers. They are not duty bound to help though, it would just be the best thing to do.
The New York Giants are paid to play football. They are not trained EMT's. They are not trained Fire Fighters. They are not even in the coast guard. They are not obligated as a football team in any circumstances to support disaster relief efforts of any kind. Disaster relief is better left to professionals of relevant fields. Being a linebacker is a great accomplishment, but has nothing to do with helping people in a time of crisis and no duty related to this should exist.