I haven’t played the first game in years (it was released in 2013 and my last go at it was probably circa 2017) but yes that’s basically the crux of it I think. The show at the end of season 1 seemed to be very faithful to how it went in the game.
I seem to recall some flashback scenes from
TLOU2 with Abby and her dad where Abby definitely knew about the situation before it went down. But that game does a lot of bouncing around and is kinda hard to follow. I think they are addressing some of the complaints of the game in the show. For example, a big scene in S2 E1 doesn’t take place in the game until pretty late and it’s as a flashback. I am very curious to see how they structure some things moving forward. In the game, you play as Ellie for most of the first half of the game and then do a hard cut to playing as Abby for the second half, mostly in the form of flashbacks. A lot of people hated that so I’m not sure how it will go in the show.