Running requires more energy simply because one is using many muscles to maintain balance against gravity. Cycling, generally speaking, keeps the body static on the saddle while only moving the legs.
Of course someone will argue outliers like standing and cranking, micro balancing in the saddle, using the arms for leverage etc... but most people, most of the time, don't do that to the extent of running. In running you are lunging forward and recovering/repeat.
To see the extent that this operates in running watch a 100m sprinter vs a marathon runner. The lack of upper body movement and reduced gait is all about conserving energy.