so jumanji changed from a board game to a video game. then the next iteration of jumanji could be a computer game or an app like imagine it spreads like wildfire over the internet.
We don't actually see Jurgen the Brutal die. We couldn't see his bare arms, so we don't know how many lives he had left, or indeed if he'd died within the game before or understood its mechanics at all. When Spencer hit his chest with the Jumanji berry and his strengths and weaknesses display appeared (in a completely different style from the other characters', with an old-fashioned gold frame, implying Jurgen has been in the game for a long time), he looked at it like he'd never seen it before. It's quite possible that after falling to his apparent death he respawned nearby, but too far away from the action to do anything more to the heroes before they left. Killing Jurgen isn't a necessary part of the quest, only retrieving the Falcon stone and showing it to the sun.
Therefore you could just open a third movie in the series by revisiting Jurgen's fall, showing him respawning and realising that the game he escaped into from real life works completely differently than he thought (or, to be fair, than it did in the form that he entered) and he isn't the only real person in it, and his reaction to that realisation setting off the plot.
Is Jurgen (mentally) an adult, an adolescent or a child? When and where is he from (is the player behind him a "he" at all)? Has he been feeding people to hyænas and so on thinking that it was only a game where he could do whatever with no moral qualms? Does he want someone to compete against?
Does he realise or discover Cyclone the black pegasus is a player? Could there be other player characters going around in Jumanji that he's unaware of? Would it make sense to tell the story entirely within the world of the game, with Spencer, Martha, Bethany, Fridge and Alex not needing to be involved?
What if someone else is a player character but pretends to be an NPC? Some mastermind moving the pieces? Someone like... Nigel Billingsley?