I played this one some time ago and really liked it. There isn't much inventory - if any - as I remember it. You mostly find clues by sensing them. The game does not hold your hand and you are on your own to solve the mystery of Red Creek Valley. There is a lot of walking around the beautiful scenery which I caught myself looking at a lot! Make sure you walk off the path or the railroad tracks and look for clues.
This is probably the best walkthrough which helps you figure out what to do. Be sure you know which keys do things like "sense." As you sense more clues, you will get more of a complete picture.
Vanishing of Ethan Carter Walkthrough