What kind of skillet is this in the picture?

It is a German brand called Turk. Fantastic quality - I own several myself and they are available in several styles. I'd recommend checking amazon.de (the German Amazon) for options.

I think it's one that they used to offer (and maybe still do) in the Shop on this site. It has a diamond-scored bottom.

Probably a wok with a handle based on appearance and the instructions in step 2 of the recipe:

"Heat a wok or frying pan on medium to high flame for 20 seconds."