Can you download games from other sites using the same method? If so, then it's a problem with the site you're going to. If not, then you'll probably need to use another method.
I know one thing you can do is you can download the webpage in its entirety, then simply open it from where it's saved. This bypasses the need for finding the original file, but limits your use of whatever application to your web browser, and specifically that page.
Another option is to go through the page source and find the actual game file, as a URL, then type that URL into your browser, go to the game file, and download it. I've done this for Youtube videos before, as well as for game files for a GameBoy emulator (I downloaded the emulator, and just needed the file).