It used to be.
Older computers (and electronics) were made with old technology. Basically, they couldn't stretch gold as far as the can now. Old motherboards, CPUs, Memory, etc used gold for tracks and contacts (terminals) the older the technology generally the thicker/bigger the contacts.
Modern electronics use a fraction of what computers did 15-20 years ago.
In fact, I remember reading a comparison which stated something along the lines of an Amstrad 8086 had the equivalent amount of gold plating/etc as 35 modern desktop computers.
It's still in modern electronics, but being realistic the recovery and processing costs would exceed any worth. Unless you're doing this in large numbers with constant supply..
You also have the issue of scrapping the non-precious parts. Again modern PCs if you look at the casing is thinner than older machines and wouldn't command as much value. Then you have plastics, etc as well.
Before the quakes in Chch I was working in a computer repair shop, we had an old guy that would come in and ask for any old parts so that he could do this 'as a hobby' turns out he was just selectively cutting away at each component and collecting up all the previous parts and selling them to a refinery in Germany. He started coming in less and less, I asked him why and that's when he admitted that he didn't really do any of it himself and the increasing shipping costs made it out to be a loss.
The other thing is, the YouTube videos that show at-home reclaiming of the previous metals never point out the purity which in most at-home solutions is pretty low/poor. I looked into doing this myself as after the quakes we had about 450 computers (notebooks and desktops) that people had abandoned at our workshop after acquiring their insurance reports, at the time I was being made redundant and was quite cash strapped and I still knew it'd be a waste of time.
So, yes it can be done.
Is it worth it? In my opinion, not really.