Nichol, who is also the Demons' backline development coach, became involved in the feisty altercation when he tried to impede King, who was busy wrestling Demon midfielder Jordie McKenzie.
AFL Football Operations boss Mark Evans said a club runner may not make contact with an opposition player.
Under AFL regulations, a club runner is allowed to enter the field "for the sole purpose of conferring briefly with the players of his club (and) … must then immediately leave the playing surface", and may not interact with opposition players or the umpires at any time.
King was fined $2100 for his part in the melee, while McKenzie accepted his $1600 sanction for a first offence in engaging in a melee.