I am an old (really old) gamer who got away from the life years ago when I had kids. Now I am finding renewed interest. I've been a member of GOG for a couple of decades and they recently sent me an e:mail regarding some classic games they had for sale. I purchased several of them. My problem is I can only get one of them to actually play. They're all paid for and I have done what I assumed would download them onto my PC They show up as icons on my desktop, but when I click on them, they simply take me back to the page describing the game. Somehow I managed to get Deus Ex to load and play, but it is the only one. Can someone please help this old timer?

I will help you, but first

What is your Operating system. Linux or Windows 10/ 11

You used galaxy client as downloader or you downloaded offline installers?

Also name games that dont work and one tha work.

Also helps to what he did to get said games. Because whether galaxy or a web browser, there are a few ways to make mistakes.

A common annoyance is the crap web design that screws with the less informed customers. Making a big dumb blue button look more attractive than the actual offline installer. The stuff people actually aim for in a browser.

edit= typo

That sounds like you're using the client and you're referring to its display as the desktop?

By your profile game history I assume the not launching games are System Shock Enhanced Edition and System Shock 2?

Let's start here.
You hovered you mouse over [Your Account]
then clicked [Games]
--> [Game's Name]
scrolled down to [Download Offline Backup Game Installers]
--> [Game's Name (Part 1 of X)] (<-- the ".exe" - file)
--> [Game's Name (Part 2 of X)] (<-- a ".bin" - file (not all games have those)
etc.,...

After you downloaded ALL the files to your computer, you double-clicked on the ".exe" - file to install the game on your computer, right? So far, so good. That should not happen.
At least not, if you used the offline installers (as described above).

Don't use Galaxy.
You write you're a "really old gamer"...you don't want Galaxy, trust me.
From everything I read about that program here on the forum, it's more pain than gain and not worth the hassle.

Simply stick to the offline installers - they're basically what you're used from earlier in your "gaming career", only that you have to download your game from GOG first, instead of popping a CD in.