When I ran the Open Xcom exe it would not recognize the GOG version of the game and it said the installation failed. Any ideas on how to install Open with the GOG version?

I was having trouble with the installation too, something about not being able to download a patch, connection timing out or something, and the installation failing.

This is how it worked for me, it should work for you too:

*Download Open Xcom of your choice (I tried with the Current Milestone: 1.0 for Windows).
*Then, in the download section, click on Extras and download the OpenXcom Universal Patch.
*Extract the Universal Patch zip file into the folder where your GOG game is installed (mine was C:\GOG Games\X-COM UFO Defense). It will ask if you want to replace some folders and files, do that.
*Install Open Xcom, but remove the choice where it says Universal Patch or something like that, the one that requires Internet connection.

That should be all. it worked perfect for me, I played a mission and I found the improvements really cool, it's totally worth it.. I will reinstall it tomorrow, so I can try a more recent build from the "Nightlies" choices, which is requiered for a mod I want to try, hopefully it will work fine.

Hope this was of help and you can get Open Xcom working if you haven't already. Have fun! :)

It is a very bad idea to use 1.0. It is very outdated and has lots of known bugs. The nightly builds are a lot more stable and they support both UFO and TFTD.

Thanks for the info, I was still going to try the nightly builds as it was needed for a mod I want to install, but I thought 1.0 was a more stable build, so it's reassuring to know the nightly builds are the better choice. :)

I'll just add that, yes, the nightly builds are the only way to go...avoid 1.0. 50 hours of playing the latest nightly and not one crash. Win10x64, 2560x1440, AMD RX-480, Crimson drivers 17.7.2. Install OpenXcom Extended and things are fan-tastic.