Why energy matters for light to escape event horizon?

Thanks for editing the question to provide clarification. The material you quote from the Wikipedia article is simply wrong. Note that the article has a template at the top warning that "This article needs attention from an expert on the subject." The trajectory of a photon near a black hole has nothing to do with its energy. The geodesic equation has uniquely defined solutions for a given initial position and initial four-velocity. Two photons with different energies will still have the same trajectories if they start at the same position and with the same initial four-velocity.

I've edited out the incorrect material from the WP article, and left comments on the article's talk page.