Peter, for me at least, the "Coal Oven Pizza" or, perhaps more appropriately New York-Neapolitan as the style was an Italian immigrant interpretation of Neapolitan pizzas using the ingredients at hand here in the "new world" is determined by cooking times, the crunch-chew characteristics of the crust, use of fresh mozzarella, sauce which is much more Neapolitan in style (uncooked San Marzano or other Italian tomatoes), TF, etc.
I don't feel this style and NY-Style (street slice) are the same style of pizza at all.....NY Style is almost like a bastardization of the original New York-Neapolitan style which has sadly devolved into the use of cheap ingredients, long cooking times, dried out pizzas, etc. Most of the pizza sold in NYC is akin to McDonald's, Burger King, etc (cheap, fast, comestible food made with no care).....in essence the entire style when taken as a whole is now BS, with a minute number of good examples. To be frank, the NY-Style (street style) is likely best being preserved by the "At Home Pizzerias" of the members of this board.
I personally do not feel NY-Neapolitan/Coal Oven/Elite is constrained to the fuel source only. As an example, I would consider Toby's Public House (Brooklyn-WFO) and Lucali (Brooklyn-WFO) to be New York-Neapolitan in style, just as the Lombardi's, Totonno's, John's, Patsy's, Grimaldi's Big 5 are.
Regardless of fuel source (and keep in mind opening a coal oven pizzeria in New York is very difficult do to regulations), Chau's video looks very much to be in this same style.
Of course this is just my personal opinion, which is just one person's rambling.
DiFara is kind of difficult to peg...the mixture of 00 & HG flours DeMarco uses brings a character to the crust that is not quite in this style. Kind of a hybrid almost.
Then again, at the end of the day all of it is pizza!