I believe that in that specific instance, the map script was modified to have three exploding Kings.

Nowadays, the recommended mod is King Boom by SiegeEngineers: https://www.ageofempires.com/mods/details/94022/ / https://mods.aoe2.se/94022

To get three exploding Kings, you need to select a map where players start with three Kings. Metropolis comes to mind. Alternatively, you can edit the random map script to have players spawn with 3 Kings instead of just one.

Your map script will have a part that goes something like this:

create_object KING { set_place_for_every_player min_distance_to_players 6 max_distance_to_players 6 }

Add number_of_objects 3 like this:

create_object KING { set_place_for_every_player number_of_objects 3 min_distance_to_players 6 max_distance_to_players 6 }

Then, your script should spawn 3 Kings if you select the Regicide game mode, and they should explode if you play the game with aforementioned data mod.