My son ran excitedly to me saying that there is a site that has a downloadable game for Linux. And indeed that is the case. It is a Java application and is available at: http://www.puzzlepirates.com/
I just set it up, and it does come up but is having problems logging in. Have sent an email to the webmaster.
Yes, there are flash games that will run on Linux, but this site explicitly says Linux and that has to be a Good Thing (TM).