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You don't need to improve upon all metrics, depending upon the application.

For grid scale storage, for example, energy density can be very bad; even inherent safety can be compromised because it will be operated under narrow conditions, while costs should go down.

For airplanes, energy density needs to significantly increase, while keeping safety constant. Cost can be higher than existing batteries.

The article isn't using the term 'radical' in such a sense:

"Stable radicals are a class of organic electroactive molecules that have been widely used in different organic battery systems. The first of this kind was commercialized by NEC in 2012."

This battery promises safety, but not energy density (it's only 130 Wh/kg, vs 250 Wh/kg for lithium-ion). As for cost, they don't claim anything, it's at the research stage. They claim many cycles (800) and quite low loss per cycle (0.028%).