This is irritating like hell, I bought Rebel Assault 1 and 2 and I have no idea how to play them now.

Can you give a bit more detail on what the problem is?

It's a bit more involved than that. You'll also have to download and install the games if you want to play them. You'll find the games in your game library under your account. It's part of the menu at the top of the screen. Just hover over the "ACCOUNT" option in the menu and a pop up menu will appear. Then click "Library" to see the games you bought. If you click on the icon with the name of the game you want to install you will get the option to download it. Once you've done that you'll have to go to the directory where you've downloaded the game and run the executable in order to install the game. After installing the game press the "Start" button and navigate to GOG.com menu which you'll find under the "Programs" menu. Then look up Rebel Assault 1 or 2 and click the icon for the game you want to play. It should be the icon in between "DosBox Configuration" and the "Uninstall" icon. It's pretty complicated but you should be able to do this. Or you could ask your mom and dad to give you a hand. Or maybe an older brother or sister.

The .exe files just aren't opening up to start the installation process.

That's really unusual and sounds quite frustrating. Possibly something went wrong with the download. Try downloading the install files again and I'd recommend using the GOG.com Downloader if you didn't the first time: http://www.gog.com/downloader

If the installer files still refuse to open after redownloading with the GOG.com Downloader contact support (http://www.gog.com/support). They sometimes take a day or two to get back to you, but I've always found them to be very helpful.