Madison Square Garden in NYC is owned by the same corporate conglomerate that owns the Knicks and Rangers. Because it's built on top of a train station, they have an air rights or ground lease with the NYC government. To prevent the corporate owners from selling one or both of the teams to another owner who would try to move them to another location in the NYC area, that lease has some kind of provision that prohibits either team from playing its home games anywhere in NYC other than Madison Square Garden. So when the NHL decided to schedule outdoor games at Yankee Stadium and Citi Field, the lawyers took a close look at that lease and said those games could never be home games for the Rangers.
The other angle to this is that the home team loses a home arena date for a stadium game. The NHL gets all the ticket revenue, and they pay the home team a hefty fee to make up for the lost revenue based on the average home revenue for that team. Since the Rangers have ridiculously expensive tickets and corporate suites, their average revenue for a home game is the highest in the NHL. So the NHL would much rather pay the Sabres than the Rangers in this case.