The game program installation installed registry entries as well as the Program Files, and probably some entries to My Games. Since you apparently deleted the Program Files, it appeared that the game was gone, but since you did not uninstall the game using Control Panel>Add/Remove Programs, the registry entries still exist. You have a couple of choices:
-- 1) Live with it or
-- 2) Run regedit, search for game program name, and delete the entries that you are SURE are for that program.
If you have no experience in editing the registry, you may want to consider having an experienced tech person do it for you.
If you choose to edit the registry, be very careful; deleting or changing incorrect entries could render you machine inoperable, and require either a clean install of XP, or a Repair install.