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After some thought, I'm starting to think that the Glowing Shot is the power of either Hyakuren or Teni'muho transferred into the ball rather than a part of the player's body. We've seen that this is some kind of a power shot. I'm really starting to think that it's one of the power auras being densely concentrated into the ball. Either way, it's ridiculous. I don't think one should ever forget the page where Ryoma finished training for it, with holes in trees and such. Things like this are the reason why the Chinese readers call New Prince of Tennis "Homicide Prince."
I think it's just the power from some other dimension, it's been pretty clearly stated as such. Muga and its doors don't seem to be comparable in that respect. It also seems to be a series of techniques alongside Kijin/Pirate and Black Hole (and possibly more), and those most certainly have nothing to do with Muga.
If anything I wonder if all those powers come from the same different dimension or if there are multiple.
Like, the player transmits some of his powers into the ball, then hits a SSS (or something like that, I dunno how the SSS worked). If it's a power from another dimension or not, I dunno (I kinda doubt it tho, I feel like the only players that have shown dimensional powers so far are Tokugawa and Byoudouin).
As for what "power from another dimension" means, we have no clue. The way they refer to it as if it's actually a dimensional plane where power exists to be manipulated, like the place Ryu and Ken fought M. Bison in the final episode of the Street Fighter II V anime.