I select play on my game and I get a thinking weel then nothing. WTF?

You're going to have to give us some more details than that. You don't even mention the game.

- The game?

- Your method of download? Did you use one of the clients? If so, which one? If not, did you download it from the website?

- Your specific OS?

Sorry, very frustrated. I purchased X-wing vs tie fighter on line. Then I was promted to down load GOG to play it. It shows in my library as installed but when i select "play" I get the games home screen. From there I select "play x-wing vs tie fighter" but then nothing happens

Perhaps you could uninstall GoG Galaxy and the game, then install the game with a different option.

I think using a Classic game installer will work, assuming your OS is compatible.