You don't need OOP to do anything! But in the state machine example, it provides a coherent and readily understandable metaphor (object modifies its own private state; callers can tell it what to do but not how) for the task at hand. Isn't that the goal of a programming paradigm?

These are called Abstract Data Types.

This paper describes the differences between objects and ADTs, https://www.cs.utexas.edu/users/wcook/papers/OOPvsADT/CookOO...