Air carrier ground personnel reported a gate agent walked by the parked aircraft's running engine to chock the landing gear at the gate.

Narrative

Flight ABCD pull into gate X without the self-park system being on and without both wing walkers in place. As the aircraft pulled in the Team lead signals to a agent standing on the side to go wing walk and the team lead gives his wands to the agent. Team lead then goes over to the self-park system panel and activates the system causing the aircraft to stop. With the aircraft stopped the wing walker gets into position and the system parks the aircraft. Once parked the aircraft left its number 1 engine running due to an INOP APU. Gate agents began to approach the aircraft to assist the arrival process unaware of the running engine. The team lead tried to stop them but was unsuccessful do to not having wands to sign a Stop signal and used his hands to try and stop them. By the time everyone realizes the engine was still running one agent walked under the aircraft into the number 1 engine ingestion zone to chock the MLG then turned around and went back under the aircraft and exited the OSZ (Operational Safety Zone). When I interviewed the team lead who was the marshaller he stated that he thought the self park system was responsible for guiding; stopping and controlling the movement of the aircraft during the arrival and that he was not trained to use the system. I checked with other team leads and they said something similar. The pilot also seemed to not realize the self park system was not active when he was pulling into the gate as he stopped when the system was activated and showed a wait message.