When you sit down (go on, try it yourself now), you always drop your head a bit - you have to as you are changing where your weight goes. This would mean that the camera would briefly lose your eyes - and you also need to see where you are sitting to make sure you hit the spot. By using the over-the-back-of-the-chair technique, in each example he keeps his eyes straight ahead, and so Mr. Camera sees all the more of him, making him more effective and mesmeric.
The opposite of this is getting out of a chair, when we naturally will dip our head as we transfer the weight from our bottom to our legs - but on camera this again would mean that our eyes are lost for a moment. If the camera is on you, then push one leg underneath the chair to be underneath your bottom, and use this to lever yourself up without dipping your head, so allowing your eyes to be seen by Mr. Camera all the time from sitting to standing, and for the audience to think how effective we are.
Kudos to Johnathan Frakes for an effective, if a little inelegant, technique.