I think webmaster refers to the main architect of a Web site-- a swiss army knife type who has a sense of why and how to fit the pieces together:
If you were to take a tally of webmasterworld contributors' personality types, I bet you'd find they are mostly INTP (architect), INTJ (mastermind), ENTJ (fieldmarshal) or ENTP (inventor)-- in that order of frequency. If this true, it wouldn't be difficult to figure out why the term "webmaster" continues to stick.
I'm sure of one thing -- it does not refer to the server admin and programmer alone. It refers mainly to the work of the Web-- the machinery that supports it are key of course, just as electricity and elevators are key to the design of a hospital building and would be sorely missed. There are finer points to building a good hospital than its basics though.