There's so much wrong with this chart that it's difficult to decide what to begin with. I guess I'd first point out that having an ideological bias isn't bad per se, as the source of the chart, AllSides, implies in its motto (“don't be fooled by media bias and fake news”.) Lacking a clear ideological bias doesn't automatically make you more trustworthy.
On the contrary, you can have a clear ideological slant and still be trustworthy because your reporting and verification methods are solid, and because you strive to be honest and fair. Think of the New Yorker or Mother Jones magazines, for instance. On the right, Fox News online is pretty decent, National Review is a mixed bag, but it still has good columnists, and I fondly remember The Weekly Standard, which was clearly neoconservative while holding itself to strong professional standards, particularly when Stephen Hayes was in charge (Steve has just launched a new media venture recently, by the way; it's called The Dispatch.)
But the main reason this chart is so deceptive is that it compares things that aren't comparable. Come on, Breitbart or The Federalist rags at the same level of “bias” as Vox? The Washington Examiner at the same level as NPR? Those aren't equal. Neither in terms of trustworthiness, nor in terms of ideological bias. And The Hill (The Hill!) isn't a “centrist” publication. I could go on and on, and I'm sure you will have your own pet peeves.
UPDATE: Laura Ana Maria Bostan suggests this scatter plot as an alternative:
