A game without UI is something that cannot be made. Sometimes while playing a game, you can find there is no UI within the game while the gameplay is running. But even with those types of game, you must find a UI somewhere, at least in the game menus.
The game UI could be something simple, starting from a simple text on the screen HUD, or might be something more complex, such as 3D UI elements, or even a map as with FogOfWar.
The main functionality of the UI usually is not as a gameplay element, but it is a game play helper and a method for instant feedback. UI, as a helper, might be a map or a piece of text describing missions to the player, stating exactly what he/she should do or where to go.
However, it is ...