Copying Grapher to your own machine.
In order to open files from your local machine (given the way JavaScript reads files), you will have to copy it to your hard drive. Everything else can be done, just fine, over the web.
Grapher is copyrighted, (somewhat unavoidably given the way Title 17 of U.S. Code reads), and I would not want someone mucking with the source code (unless they are a registered collaborator) or selling the thing to someone. Those exclusive rights of the copyright holder are not being surrendered by virtue of its appearance on the web and there is a good amount of juris prudence to support this claim.
But you may copy the program and use it on your local machine for the purpose of reading and writing files.
To do this from the Internet Explorer browser, use "Save As..." from the File menu.
At the same time it would be nice (for sake of curiosity, rather than legality) to know if you have copied it to your machine. So, drop me a note. (email to david.dailey@sru.edu).