Firewatch is a single-player first-person mystery set in the Wyoming wilderness, where your only emotional lifeline is the person on the other end of a handheld radio.
I would agree it's less of a "game" and more of an interactive story, but calling it shit for that reason is a bit harsh, it's a great tale. Just not everyone's thing.
So it's a video game, full stop. Just say you only like mechanically focused games, a valid opinion, instead of this absurd gatekeeping where games you don't like aren't actually games.
Totally, dude. A hike that requires light bouldering or traversal becomes a game of ideal foot placement and clambering. If you bring a camera on a hike you end up internally rating your own pictures or hunting for opportunities. You can gamify a lot of things.
Playing Firewatch by choosing the dialogue responses that paint Henry as a certain kind of person is a game. Role-playing, if you will.