To record all game sounds including chat including your own voice at the same time without having to use a separate recording device or microphone mixer, you will need an aftermarket gaming headset with microphone monitoring such as the Turtle Beach X31. This type of headset mixes together your voice from the microphone along with all the other game sounds including other peoples' voices in chat so that they can all be heard through the headset's speakers. We are going to be recording directly from the headset's speakers.
First, remove the batteries from the headset. Gently pull off the earcup padding surrounding the left speaker. This is the side with the microphone boom and audio controls. Remove the three screws surrounding the speaker to expose the circuit board. Be careful when removing the screws so that they don't get sucked into the speaker grill by the speaker's magnets. Also be careful because the speaker will still be attached to the circuit board by very thin wires.