The Forest

The Forest is a first-person survival horror game from Endnight Games. Your plane crashes in a mysterious wooded region, you are the lone survivor, and a tribe of cannibal mutants lives nearby. Your son appears to have been taken, so besides staying alive you have a goal.

The game combines building and crafting: you chop trees, set up a camp and defences, hunt, and gather food and weapons. The world is open, and at night and in the caves it gets truly creepy, because enemies can attack in groups and get around your fortifications. Every trip into the woods is a risk, but it also brings new finds and story clues.

According to HowLongToBeat, the story takes about 16 hours and a full run about 59. For a month at roughly 60 hours that is enough: you can finish the main story with plenty of room, and even 100% is nearly within reach. The single-player game works offline; online co-op is not part of the rental.