In the world of linear game design, it would hard to get much more linear than this: your travel options are limited to f (forward) and b (back), as you follow a path to your appointment with destiny. At each stage, you confront those who would stand in your way, which usually means relying on your six shooter.
I would expect Gun Mute to appeal to people who enjoyed the recent combat-puzzle games Slap That Fish or Attack of the Yeti Robot Zombies, but I think it is a bit better-designed than either of those. The puzzles generally seemed fairer than the ones in Slap That Fish, and it's clearer from the outset what the player is supposed to be doing. Meanwhile, the environment is more richly imagined than AotYRZ, not only because the player is allowed to look around and examine objects, but also because some care has been put into developing a coherent setting. This is a strange vision of a post-nuclear society which has gone back to old-west manners and mores, except with a somewhat more modern view on acceptable romantic pairings. There's also more of an overarching plot: nothing very complicated, but satisfying for the size of game this is.
It's not a long game (and the gameplay premise would probably wear thin if it were), but I found Gun Mute novel and enjoyable.