This is a great start to something more. The current version was understandable from the beginning to end while playing completely blind. I do have some nitpicks, such as not knowing exactly what resources I currently have, maybe a button to check bullets, food and water respectively.
Also when passing a house, it would be nice if the character stopped "moving" and a long press or short press would determine if you went in to search or not. This would give the player a chance to listen to their inventory and decide if they should risk going into the house.
Another thing that would be nice is a more clear indicator of progress and how much time is left. Again another button combo could be used (I know you are doing a 1 button game, so maybe short press, long press, double tap, triple tap ect.. could be used) Or maybe this info could be shared at each time you reach a new house, "Man!, I made it about halfway to the camp but I only have 2 minutes left to get there, let's see, I have 1 water, 1 food, and 4 bullets left". With one sentence and you have all your info!
I think this game has a lot of potential, so please don't see my feedback as negative, I hope it can help you make the game feel more fun and fair to the player!
Great work and thanks for sharing your game.