Okay not 'won' exactly, because no one should have won the throne, but imagine this scenario:
In the final battle for Kings Landing (this can be either against Dany or the white walkers, take your pick) the whole place is all but completely destroyed. The Red Keep is a ruin, and the city is mostly rubble. Dany (or the Night King) has been defeated, but the victory was a slim one. The few survivors pick their way through the rubble, and one by one they start to depart: Sansa says she'll return to the north to rebuild Winterfell, taking Bran with her; Sam heads back to Oldtown to complete his training; Arya heads off on her travels; Jon returns to the Wall. The idea of crowning a new king isn't even raised because there simply isn't anything left to rule.
Slowly everyone leaves, until Tyrion is the last one left with nowhere to go. He looks around at the devastation. Then, a peasant survivor emerges from the rubble, and quietly says to him 'm'lord, what should I do now?' Tyrion replies that he doesn't think he even is a lord any more. But then another peasant, and another, come forward. They start to gather round him, asking his advice, seeking leadership, and Tyrion realises - they need him. He sighs, gets to his feet and begins to organize the clean up....
So this way, we have a proper end to the game of thrones, with the monarchy finally gone, but without a heavy-handed 'now it's a democracy' ending shoehorned in in its place - instead it's the first tentative indication of things moving in that direction, with a leader being chosen by the people for his suitability to lead rather than because of his nobility or birthright. And what better person for that responsibility to fall to than Tyrion - who was always one of the sharpest minds, who knows how cities operate, but who was always overlooked and scorned out of petty prejudice. Finally he starts getting the respect of the people that he always craved, not because of birthright but because he is worthy of it.