What are the mushrooms used in this (video) recipe?
I'll elaborate on Joe's answer some. It's a little known fact that button mushrooms (also called common, white, or table mushrooms), cremini (crimini, baby portobello, baby bella, brown mushroom), and portbello (portabella) are all the same species. Specifically, agaricus bisporus. The difference in appearance and taste is based solely on maturity. The youngest are white button mushrooms, and the oldest are the big portobello mushrooms. There can be slight differences in skin color for the portobello's, though it tends to be darker than the stark white of the button.

The mushrooms in that video are most certainly fully mature agaricus bisporus, a portobello.

It's a safe bet that anytime you see a mushroom being substituted for a "steak", that it will be a portobello. They have a rich meaty flavor and texture that is perfectly suited for this.