Not only would Stevens not be the chairman of the Senate Committee on Commerce, Science and Transportation in the new (111th) Congress, he hasn't been since early 2007. After the 2006 elections, when the Democrats took over the Senate, Daniel Inouye (D-HI) took over that chair, and presumably will continue to hold it through the 111th Congress since his party remains in power. Stevens is currently not even the ranking minority member of the committee; that title is held by Kay Bailey Hutchison (R-TX). He does still have a seat on the committee, though. AFAIK that seat will be taken over by another Republican senator, not by Begich. Begich could get appointed to one of the committee's majority seats, but as a freshman senator he's not likely to get anything very juicy.
Whether or not Inouye, Hutchison or Begich "understands something about the Net," I do not know. But in any case, that sentence in the story was certainly irrelevant, just an excuse to get in a cheap "series of tubes" dig.