Deleting files manually is generally the worst thing that you can do when trying to uninstall a program, as there will still be no end of registry entries remaining which you can't really safely delete unless you know what you're doing. Those registry entries are what will be making the game think it's still installed.
If you can, reverse the deletion by restoring them from your recycle bin. Then, try to look for an uninstall program within the Psychonauts directory itself. If you can't, try going to add/remove programs in Windows' control panel to see if there's anything there related to Psychonauts.
If the files are gone for good, go to add/remove programs anyway. Sometimes Windows will let you automatically delete registry entries if it cannot find the original files, although this is not guaranteed to work. If it doesn't, the only real final route I can recommend is to post on the official Majesco support forum