I'll go out on a limb to say, I'm unaffected by how this does or doesn't match up to the ultra-popular video game.
I would just advise to see it. When the episode was over, I paused the TV and sat to take it all in.
What a portrayal by Nick Offerman (who is coincidentally married to the openly bisexual Megan Mullaly). Deeply moving.
https://www.cnn.com/2023/01/29/entertainment/the-last-of-us-episode-3-review/index.html
...the start of this article directly addresses the game vs TV characters:
https://www.cnn.com/2023/01/30/entertainment/last-of-us-bill-frank-episode-3-cec/index.html