The story of Hatris takes place in a hat factory where hats are stacked on mannequin heads to be shipped out. The player's goal is to stack five hats of the same kind on top of each other before they fall down and get shipped out, earning a cash bonus. As the game progresses through multiple levels, more types of hats appear, making it harder for the player to complete their task.
The gameplay involves stacking hats on mannequin heads, with the goal of getting five of the same kind stacked together before they fall down. The game gets progressively harder as the player advances through levels, with new hat types being introduced. Players can also use stored aid from avatars Alexey Pajhitnov and Vladimir Pokhilko to help them complete their task.