I would like to play Super Mario 63 on my work laptop, but not in a browser. I have only found the game embedded on a site. How can I download it?
To generalize: there are flash games you are allowed to download and distribute and there are flash games which are not allowed to download and distribute,
Companies that allow you to make a login and download flash games to play them locally and/or copy them to your own site (i have downloaded about 45.000 flash games) among others:
If you want to have a lot of options around this like auto downloading etc..., then install XAMP, WordPress and http://wordpress.org/extend/plugins/myarcadeblog/ and you can run this semi automatically in other words: it acts as a GUI for all of this. Notice that XAMP installs a local webserver that enables you to play the games on your localhost.
You need to have the Flash Player Projector for your platform. Depending on the installer, there might not be a way to get around installing, especially on Windows. Mac OS X installer packages can be manually extracted, so no big deal there. Windows installers are trickier and often do registry updates (the big deal breaker).
If the machine in question is a Windows machine, try installing the Flash Projector on a Windows computer you admin and then copy the Projector application to the other computer and see if that works.