OK, I am back. I have done all the above. There is no indication that the game is downloading. Am I missing something.

Which game are we talking about?

Did you actually click on the download links ("F.E.A.R. Platinum (Part 1 of 3)", "F.E.A.R. Platinum (Part 2 of 3)" and "F.E.A.R. Platinum (Part 3 of 3)"), or did you just select the OS?

click on each part 1->3 (wait before each part is downloaded to proceed to the next)

I don't want to confuse you further but the Galaxy client may be a good idea for you since it does all of that for you. You just need to install the client and you are good to go for all your GoG games.

An alternative to the good ol' "do it yourself" method of installing is using Galaxy, GOG's answer to the Steam client. It still a work in progress, and as such, has its own quirks and problems, but if you know next to nothing about installing stuff and would rather have a program manage your installed games for you, you might want to check it out. (Just click the blue 'Try GOG Galaxy' button that appears in any game's "box" on your GOG library shelf, or the purple banner on the front page, to find out more.)

Ok, Problem solved. I am downloading. Thank you heaps.
Thank you. This was the advice that solved my problem.