First off you should know that your iPod ClickWheel Games were sold to you on a one time only download policy with a reminder to backup your files against just such a disaster as you have encountered. If these were physical products that you had broken, lost or had stolen from you then you wouldn't expect a free replacement from the store you bought them from so why are you angry at anyone other than yourself now?
FWIW Apple has changed the repeat download policy for music and TV shows within the last year. As far as I know iOS apps have always been subject to repeat download, but in all cases subsequent downloads are permitted on the proviso that the item has not been removed from the store. In other words you should still backup any data you care not to lose.
While the ClickWheel games are no longer on sale it might be possible to request that they are requeued for download to your account if you explain the circumstances of your loss and ask nicely. Conversely it could well be the case that the store support staff simply have no ability to grant such a request whether as part of store policy or because the files are no longer held on their servers.
I've successfully extracted media from iPods before now, both with third-party software and a brute force approach which simply copies off everything and then lets iTunes rebuild it from tags. I've not worried about extracting games before but a quick search of my iPod hard drive shows no signs of the .ipg files. What I did spot however was the three Games_XX folders in iPod Control. Since we know that it is possible for iTunes to transfer a game from a device into an authorized library that is missing that game there ought to be a way to do it by hand. Having previously determined that iMovie projects on an iPhone are actually .zip files containing the resources and control files of the project it seems a safe bet that .ipg files are the same. Sure enough I made a copy of one of my existing games, changed the extension to .zip and had a look inside. The contents match the contents of one of the \iPod_Control\Games_RO\<5 digits> folders on my device. At a guess zipping each of these folders up into a regular zip file, changing the extension to .ipg and then importing the resulting files into iTunes ought to work. Time to test the theory...
Time Passes...
OK, I've tried taking one of my existing games from the device, zipping it up, and changing the extension. I used XPs built-in "make a compressed file" tool but it produces a different sized output to my original ipg. When I tried to import it into a test library I got a 39 error so we're close, but no cigar. I don't have time to repeat the experiment using WinZip and different compression options but there is a reasonable chance that one of them might work. If you can turn the folder into an importable .ipg and you have authorized the computer to the account that originally purchased it then it should work.
Good luck.
tt2