The chart is not authoritative, and disproves its own reliability. It shows Daily Kos "above" Fox News, which is absurd. Media bias estimates, like "fact checks", should be taken with a large grain of salt.
Using the Pew survey results I linked earlier, you can apply your own judgement/correction to the chart.
1) The survey shows an increase over time in the polarization gap between the median Democrat frame of reference ("D") and the median Republican frame of reference ("R").
2) The evaluation of "neutral" depends on frame of reference, and one of the frames has a much greater "velocity". From D, it looks like Republicans are becoming more extreme. From R, it looks like Democrats are becoming more extreme. From the survey animation, it is clear that the net shift is overwhelmingly due to the movement of D leftward. Furthermore, if Republicans (conservatives) were truly becoming more extreme (commonly cited myth among left-leaners), it prompts the question "compared to what/when"? Are Republicans more conservative now than during the Reagan era? The Eisenhower era? Common sense suggests that on a host of issues (tolerance of divorce, acceptance of single parent and other non-traditional families, acceptance of homosexuals open in public life, tolerance of other cultures, publicly-funded health insurance/care, etc), conservatives are also moving leftward over the long term.
3) X-axis: The chart's x-axis assignments are not static. Because of the increasing polarization gap, an information source anchored to the political centre would, over time, be perceived as rightward drifting seen from D, and leftward drifting seen from R. If complaints about the perceived bias of a source are one-sided, it suggests the source is moving along with whichever frame (D or R) tends to think the source is "neutral". NPR, WaPo, NYT, and Guardian are examples of sources which have long been accused by the right of left-leaning bias which should properly have them positioned well into the "skews liberal" zone. The handful of times I have read of an organization like NYT being accused of leaning right, it has been from someone occupying a position well to the political left (way out past Sanders Democrats).
4) Y-Axis: The categories rated as "Complex Analysis" or "Analysis" deserve to be positioned above "Fact Reporting" and "Original Fact Reporting". Analysis - even partisan analysis - is more accurate (more time to assess events and sift evidence; more deliberative and less reactive to immediate events). Importantly, the writers for "analysis" organizations spend a fair amount of time responding to each other, highlighting errors and omissions. I don't find the wire services and major "fact" media all that reliable when it comes to accurately reporting "facts", and most act as information gatekeepers, which militates against their being slotted in the "neutral" column. (You can see it when organizations on one "side" are seized with an issue of the day, and barely a peep emits from organizations on the other "side".) Broadcast media convey almost no useful information at all in the time available; I find them to be a waste of time.
YMMV.