I don’t believe Joel will die as soon in TV show, at least not as soon as the second season. They’ll probably string along his character’s ultimate conclusion more towards the end of the series.

In my experience, TV/Movies adaptions are not always a 1:1 copy to their original derivative. I’m sure there are dozens of examples that I could reference to support this theory but the one that comes to mind at the moment is the TV show “Dexter” in comparison to the original book. In the book, Dexter literally had actual superpowers and was hunted by demons, Brian and Doakes Survives, Debra has a son, Cody has a “Dark Passenger,” ect.

The writers would probably take some creative liberties when they map out the future seasons to extend the story’s duration beyond the game, so after the first season, I would expect some detours from the original source trajectory.