Pedantic, but if it's an Amiga 2000 (which it appears to be from the video) then this can't have been running since 1985, as the Amiga 2000 was released in 1987. But the guy does say the computer came from eBay, so perhaps this is a replacement for their original Amiga.
I'm not sure how the RF interface works, but it it uses a zorro card, the A2000 would be the first computer that could run it. If it used serial, the even a A1000 would be a possible system.