He lives with my husband and I. Also, we have guardianship of him.

Come on. There is the letter of the law, and then there is common sense. If this is really a case of a family member living in the same house, I seriously think it's ok to share the game with them. If the son was to afterwards "share" copies of the gaem with his friends then we have a problem.

Then, in my personal opinion, just go on and install it on his device. I don't see a problem here (unless you want to play multiplayer and the game is one of those needing distinct serial keys to work in multiplayer mode).

As said before, simply download the installer, put it anywhere it fits on (thumb drive, DVD, etc.) or transfer it via local network or download it directly on his device with your account and install it on his computer. Since the games are DRM-free it works simple as that.

According to this: https://www.gog.com/support/website_help/downloads_and_games
It's ok to install the game on any computers inside your own household.

Or, if they don't necessarily trust him not to share it around, she or her husband could install it on his machine themselves from a flash drive, meaning he might not be able to copy it (unless he know what he's doing).

I'm afraid that's a misconception (regarding most legal systems). When you buy virtual goods (games, e-books etc.) you generally only buy a personal user licence. Where when you buy a physical copy, you also get ownership of the physical medium. That's why you are allowed to sell, gift or lend the medium (you are the owner), but not a user licences (once it's bound to you) because it doesn't contain actual ownership of the data.

Legally, you're right. But GOG have stated off the record before that they don't mind games being treated this way.

If it's same household, then as others have said, treat it like a book or a board game or a toaster or an ironing board: even if it's "mine", anyone in the house can use it. If your son has his own household, then sharing it by making multiple copies is a no-no.

I totally agree. It's what I've said above.

I wasn't talking about laws or licenses (hence my comment about obeying the spirit -- while disregarding the letter -- of the rules). I was simply talking about ethical use of goods for which one might have payed a purchase-level price. For legal reasons, GOG can't officially condone this type of thing, but several of their staff have mentioned sharing games with friends as being one of the major advantages of DRM-free, and one of the things they missed about the old days. (I think TheEnigmaticT might have even publicly used the "book analogy" as something that he personally thought was OK). I think the "book analogy" is a good guideline...but only if the person to whom one is lending the software is trustworthy.
Edit before posting: ZFR ninja'd me (much more succinctly, too), but I might as well post this anyway. :)

Thanks to all of you for your comments! Well, I guess I'd better decide. Wish me luck.

Need to take turns though.