At 1:52 they don't mention the hardware specs also can't tell if it's an Amiga or an Atari. I don't think it's a Acorn because the price would be more expensive.
If they had mentioned that the NeXT came with 8MB RAM compared to the 1MB RAM with the Atari 1040ST, the licensing cost to AT&T for a UNIX license so they wouldn't get sued for using BSD (CYA Cover Your @$$) Or the new Optical Media disk format.