i have just come across this website whilst trying to purchase roller coaster tycoon, which i assumed i had to play. I have no idea how to play after purchasing it .. have a made a mistake ??

Hold your mouse over your username at the top of the web page. A drop-down menu should appear. Select "Games", and this will take you to your game library. From there you can select the game you bought and access the installation file(s).

What do you mean with "how to play".
Did you download the setup from your account library? Did you click on it?
(and maybe you want the Galaxy client too)