Here’s the definition of BBQ:
Barbecue or barbeque (informally BBQ in the UK, US, and Canada; barbie in Australia; and braai in South Africa) is a term used with significant regional and national variations to describe various cooking methods that use live fire and smoke to cook the food.
Sounds like barbecue to me.
If you forward to 9 minutes into the video, you’ll see plenty of smoke. A minute later he covers the grill ... so the steaks get cooked with smoke.
That’s the very definition of BBQ — live fire and smoke.