All muscles work in contraction: they get shorter. So the triceps also work by getting shorter. Because they're on the outside of the joint, when they contract, the joint extends: the arm straightens.
So, in order to activate the triceps, you need to straighten the arm: to extend it against resistance. It's like banging your fist on the table, or tenderizing meat. Whack! Outside of the gym, you could try raising yourself out of a chair using only (or mostly) your arms.
In the video, you can see him pressing down (and away) on the opponent: expressing force by attempting to straighten the arm at the elbow joint. If the opponent did not resist, and the teacher kept going, his arm would become straight at the elbow.
You can look up tricep exercises, but they are all based on the idea of extending the arm against resistance. If you want to learn how to activate the muscle without any resistance present, you should first do it with resistance, then try to recreate that sensation without resistance. It's hard, so I'd be patient.