The SFWA's article on the Hugo Award's new eligibility rules summarizes the changes for semiprozine and fanzine categories:

The answer to the general question about whether genre websites, including blogs, are eligible in principle is clearly yes, since the rules now explicitly permit works published in other media in several categories.

For more on what web sites and blogs may be eligible, SFWA defers to Vincent Docherty, Administrator for the Hugo Awards, via File 770's article on Hugo's Award's online publication eligibility. There, Mr. Docherty gives his approach to handling the knotty process of interpreting the new rules while giving due consideration to past rules and past administrators' practices. He says:

Under the revised rules, a web-only publication of an individual work, or series of issues of a work, would certainly be eligible as a Fanzine, Semiprozine or Related Work, depending on whether it satisfies the specific category rules. There are hard boundaries between Fanzine and Semiprozine: a work either meets two of the five tests, and is therefore a Semiprozine, or it doesn’t, and so is a Fanzine.

Go to the File 770 article for a glimpse of this rather interesting process.