That is a correct, and usually preferred way to connect a button.
The tutorials on official site are not always the best ones around. Both will work and will not damage the Arduino.
In instructables tutorial an internal pullup resistor is used instead of an external pulldown used in official tutorial.
There are certain benefits to using this approach, such as lower part count and avoidance of taking a 5V line to the button which reduces the risk of accidental short circuit.
There is also one drawback - the logic is somewhat less intuitive. When the button is not pressed, digitalRead will read HIGH, and when the button is pressed, it will read LOW.
You enable the internal pullup with
pinMode (pin, INPUT_PULLUP);