Angband, Nethack are a good example of a very simple turn-based game. These require no loop whatsoever in your code. User input comes from the keyboard which is handled by the OS, so you just let the OS notify your application and when a keyboard event occurs, and your functions otherwise know nothing about timing loops, and need not do so.
Battle Chess is a turn based game with real time animation, movement etc. Clearly, a loop is once again the basis for responding to user interaction. In this case it is also used for animation, gradual moves between tiles, special effects, etc. (possibly even for sound). But the difference here is that while such a game is fundamentally loop-based, it is preventing you from supplying user input for those periods when a move has just been made and your knight is fighting the enemy bishop: it just controls when & how you are allowed to supply input. Otherwise, it operates much like Pong, CoD etc.
Loop-based / real-time systems are required for any reactive/interactive system. Event-based systems, while often appearing very different to real-time systems, are actuallyoften fundamentally associate with, if not driven by loops, and indeed often co-exist alongside themloops in various different forms.