Loganspire: I purchased two games today for my kids from GOG and one of them I was able to get to work on the device I downloaded it on, and transferred it to my Desktop and it also worked there as well.
Did you transfer the installed game, or the offline installer files? How did you download and install the said games on the first PC?
You must first realize there are basically two different ways to obtain (download and install) your purchased GOG games. You can even use both if you want.
1. Use the GOG Galaxy client. With this you can tell it to simply install the game from your online GOG account, in which case it downloads the needed files and installs the game for you. This is basically the same way you use a Steam or EA Origin client.
2. Download the offline installer (one or several files, depending on the size of the game) to your PC, and then run the installer yourself in order to install the game. You can download these offline installer files with various tools/clients, e.g. any web browser (Edge, Internet Explorer, Firefox, Chrome, whatever), or many third-party tools (gogrepo.py, lgogdownloader), or even GOG Galaxy has an option to download the separate installer files ("backup").
So if your intention is to install a game on several PCs in the household without having to download the game several times, then stick to option #2: download the offline installer files, copy the installer files to all the PCs, and then install it on all of them, one by one.
Copying the already installed games (either with Galaxy, or installed with the offline installer) to another PC might or might not work, depending on various factors. So you shouldn't really do it that way, if that is what you have done so far.