If I understand correctly, it looks like this is just evidence corroborating the existing stance?
After the antioxidant hype and supplement boom yielded no health benefits, there have been multiple large studies showing no effect or negative effects. They can remove benefits from physical exercise and increase cancer risk. Vitamin C can remove benefits from exercise.
Overall the risks and benefits are small, but basically they are all useless. If studies show benefits, it can be because some of the subjects suffered from deficiency. You should take them only to treat vitamin deficiency or increased need. Taking more and more of the good stuff is not automatically better.
There was another paper that showed dosing with supplements prevented improved fitness as well.
Oxygen radicals do cause damage in the body, but they are also important signals and invoked in programmed cell death.
And the concept of "anti-oxidant" in general can be misleading with respect to the mechanism of action. It isn't simply the anti-oxidant effects of polyphenols that are responsible for the reported benefits.