Fujitora thought Marines have no right to play hero, being a part of the World Government, who have plunged the citizens of Dressrosa into the tragedy in the first place, and hence would be playing god.
Hence why he refused to go after DD himself, hence why he pretended that Sabo is stalling him to enable Luffy to beat DD, hence why he also did not do anything regarding birdcage except stall it a bit.
Of course it´s anybody´s guess when he would have interfered if Luffy had lost.