From the web archives of the paper—here is the Sunday June 27, 2004 edition: http://web.archive.org/web/20040627044226/http://eastandard.net/
I do not see this story there.
On the page you linked, if one hits “home” BTW, you get a header Monday July 26, 2004.
It’sa not dispositive but adds further to mu belief that this is a hoax.
One thing you need to understand is that whatever it is, it is not a hoax. This is material from 5 years ago, long before anyone gave a crap about Obama.
The wayback machine has been around a very long time and is reliable. The front page has a different date because that is the date it was archived.