How long do I pre-heat a whole chicken for on the stove before placing it in the oven to roast?

It is doubtful that the "temperature is penetrating"...whatever that even means in this case. The temperature ultimately has to be at least 165 F (74C) in the breast. Placing the chicken, on top of its wings, on its side, in a pan on the stove top is not going to speed that up all that much. Especially for the upside facing part. I could see making a use of a browning step (particularly if you are going to cover (and steam) the bird in the oven), but he doesn't evenly brown the bird. He turns the bird partway through the cooking, however, to brown the other side. I am suspicious of his process, but I would say, if you want to re-create it, I doubt it is on the stove top for more than a few minutes. Brown the skin, then place in oven.

Other than browning the chicken, starting it off on the stove gives the dark meat more of a head start before it goes in the oven, because dark meat has plenty of fat and is often better when "overcooked" compared to the breast. What temperature the thigh area reaches doesn't really matter, you just want to take the temperature of the breast near the end. I would brown the dark meat for 5-10 minutes, then put it in the oven.

Adam Ragusea uses a similar method for roast chicken, who recommends 10 minutes on the stovetop.