Obvious answer: Newt still is, for better or worse, someone treated as a Serious Player by his fellow Republicans, while Wright and Foley certainly are not treated that way by their fellow Democrats.
We're talking about a disgraced, scandal-plagued politician who was forced from public office -- by his own party -- more than a decade ago. What difference does it make if he trashes the president on his Twitter account?
Remember Jim Wright and Tom Foley? They were the House speakers before Gingrich. If they had a few tweets saying supportive things about the White House, would CNN have run an item about their comments, passing them along as self-evidently newsworthy? If the answer is "no," and I think reasonable people would agree that it is, then CNN's piece yesterday is absurd.
Now, the real question is which way the causal arrow runs: is Newt taken seriously by Republicans because he's treated as important by the media, or the other way around? The former is problematic, but the latter is entirely healthy. I think most people would agree that we want the parties to pick their leaders, not the news media.
And the evidence, such as it is, supports the idea that the media are following the parties, not the other way around. Bill Clinton is treated as a respected elder statesman, because the Dems treat him that way. Dan Quayle is treated as a washed-up nobody, which is roughly how he's treated by the Republicans. The GOP may be foolish to treat Newt with respect, but that's not for CNN to decide.
A tougher question is whether, how, and how often reporters should remind people of the baggage that Newt brings with him; as Benen says, Newt is a "disgraced, scandal-plagued politician who was forced from public office -- by his own party" (and that's not to mention that he's a total fraud). I don't know that I have an answer to that one. I'm sure liberals would be happy if CNN noted Newt's scandals every time they quoted him...but I'm not sure how happy they'd be if CNN also included Monica Lewinsky in the story about the Big Dog's trip to North Korea. On balance, I'd say that reporters should try to follow the lead of political elites, rather than trying to impose their own judgments in these areas. Since Republicans have apparently decided to pretend that Newt isn't a disgrace and a fraud (or perhaps have forgotten that they once knew those things), I don't see a lot of harm in the networks joining in, at least as long as Newt isn't a candidate for anything.