[acherion]

The machine depicted in the clip is an Apple IIe, which first came out in 1983. But this might not be a 1983 model, because the monitor depicted with the machine is the ColorMonitor IIe, which came out in 1985. Because it's a computer used on a set for a TV show, it's possibly a loan machine, perhaps from Apple themselves, so it was likely supplied as a new computer + new monitor combination. So I'd hazard a guess and say this setup is from 1985 or later.

If we take my previous assumption further, the Platinum IIe was released in 1987, which came with a numerical keypad built in, and looks distinctly different from the IIe. Even though this Youtube clip is 240p, you can distinctly see that there is no "divide" in the keyboard, so this is definitely not a Platinum IIe.

I would say this machine was manufactured between 1985 and 1987.