You are confusing state labels with state outputs. The _ _ _ binary numbers are just labels for the state. It would be used as a register in your state machine just so your state machine knows what state it is in. It isn't actually an output. The _ _ binary numbers are the actual outputs that each state uses to control the H-bridge that drives the elevator motor.
In some state machines the state name IS the output but in general that isn't true. In general, each state can have outputs that are the same as other states. What makes a state unique is where it sits in the state machine sequence, not it's actual output. Obviously you want the elevator to be able to have a "stop" output on all floors and not just one and only one floor.
So you have to sit down and go through the state machine diagram you have and figure out if the motor should be stopped, going up, or going down at each state. (Hint, it's already done for you! Notice how each state has a _ _ _ binary label as well as an English label that is the floor number, up or down?). He could have just as easily written "00" or "11" instead of "First", "Second", or "Third". Or he could have just as easily written "10" instead of "Up". Or he could have written "01" instead of down. But then it would make it hard to understand since you would ask "Why is the state output 10 for this state?" Instead he writes it so you know what the state is trying to do so you can modify the state output to perform the same result if your H-bridge requires different control signals.
Do you understand?