This neologism started off life as a typo but I believe it deserves a better fate. Webiste claims 930,000 Google hits in April, 2007 which means that it now deserves to be taken seriously. The meaning I feel that best suits the word is "a lover of Websites" i.e. a Website-ophile.
I've worked with half-a-dozen Web-designers before, but I have to say that Joe is a real Webiste and I'd never work with anyone else on a project again.