You seem to be suffering from three problems here:
- A lack of understanding how the button's pins are configured
- A lack of understanding of how breadboard works
- A strange notion (that I have seen around a lot recently for some reason) that a button needs to be driven from an output.
For the button's pins you should know that the pins are paired on the long sides. That is, if you hold the button so it is in "landscape" orientation (wider than it is high) the two upper pins are joined together, and the two lower pins are joined together.
Breadboard consists of strips of connections which, in your diagram, would be running horizontal. Pins plugged into holes horizontally in line with each other on the same side of the board (the gap in the middle is a gap in the connections too) will be connected together.
Finally for the wiring of the button. Nowhere in the tutorial you link to does it ever mention connecting the button to two IO pins. The button should only be connected to one IO pin. It also connects to +5V and, through the resistor, to ground. Wire it up exactly as it shows you in the tutorial and make it work like that before you try fiddling with it.