I don't see it as a spiritual successor any more than any other post apocalyptic show. The Last of Us (based on the game and the show so far) is pretty much devoid of the characteristics that defined The Leftovers like the complete mystery/lack of interest in solving that mystery, the high concept storytelling, the focus on the existential angst of grief rather than processing it and moving on etc.

While it feels like blasphemy at this point, The Last of Us has way more in common with The Walking Dead than The Leftovers. The Last of Us is likely to be a Game of Thrones level HBO mega hit while The Leftovers was a specific critical darling with a devoted but modest fandom, and there's a reason for that.

TLDR: TLOU wouldn't make "International Assassin."