Tywin pouring Tyrion wine (after withholding it several times in the past) was a great visual payoff to show the shift in their relationship and his newfound respect for his son's strategic mind.


I thought it was his realization that he has one son left. And that's Tyrion. In the book, it's a powerful moment for Tyrion because he realizes Tywin has given up Jaime for dead. It's not that Tywin wouldn't throw Tyrion over in a heartbeat if Jaime returned, it's just that right now, he's run out of sons. And it helps that TYrion isn't a fool.