So I just went and searched for Wii Nunchuck pinout and it seems like your PINS are not connected as in your diagram. It is possible that you numbered your pins in another order but you should cross check.
What the guy explains is that you can connect +3.3v to PIN 2 or 3 it does not matter because internally they are connected. This is a sensing PIN for the Wii. Pin 1 is SDA and PIN4 SCL
Another thing is that the Pi runs at 5Volts and this WiiChuck at 3.3Volts. (But I think some other ones run at 5Volt - I saw some a few with 5V markings)
Any way even if you are powering the Pi on the GPIO 5v pin and then the Nunchuck on the GPIO 3v3 you might have a power limitation problem on the 3v3 rail. A computer PSU will have 3v3 on the Orange cable and 5v0 on the Red cable. Keep yellow 12v0 away form the Pi. Connect the GND direct to the PSU as GND over current can also cause issues.
Double check you do not have a short somewhere or that the pins are mixed up.