I think you will find that in a multi user environment, the only person with "run as administrator" in the right click menu, is the administrator.
But if I am Administrator, shouldn't "run as administrator" simply be... "run"?
No. In Vista, Administrators no longer have full administrator privileges. They use a split token technology that allows you to temporarily run that program enabled to full administrator after you click on a UAC prompt. It's done this way to maintain as much compatibility with older apps as possible but provide windows with the security advantages of Unix, Linux, and OS X type systems, where no-one runs with root (administrator in older windows versions) privs.