@SteveClough @saltphoenix IIRC archers have to "follow through" with their bows for maximum power while the kick on even a small pistol is greatly reduced with a two handed grip. I believe this specific event calls for a single handed grip, but as for why my best guess is that the air guns they use have such a small kick that a second hand wouldn't add more stability and this is more a test of pure markmanship than any weapon specific proficiency.
@mdstevens0612 @saltphoenix It is more that the bow has to be held loosely not gripped. and you have to stay in position until after the arrow has gone - which is fractionally after the string is released, and the power of the shot goes through your arm.