Sometimes the tutorial recommends a pull down resistor, sometimes not. How do they decide? I see this with PIR sensors. The adafruit uses a pull down resistor, but plenty of other ones don't.
Inputs on micro controllers can float if they are open. A pull down resistor biases the pin to ground so when your switched 5V is open, the pin sees ground, when the switch is closed, the pin sees 5V. There is no in between.
To answer your question, sometimes it works without a pull down resistor, but it is best practice to use one.
Another common practice is to use the internal pull up resistor on the microcontroller and instead of switching 5V, you switch to ground.
Sometimes the peripheral circuit has its own pullup resistor installed. In that case, you don't need one on the main board.
But the circuit you posted doesn't have a separate circuit board. So the top circuit probably enables the internal pullup resistors in the microprocessor, in the program. They are both pull up circuits, not pull down.
Grumpy_Mike:
However, if the output of the device is a logic signal then there is no need for a resistor because the logic signal provides a solid zero and one.