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The page on Heraldic Chess, from which this piece comes, was posted six months before the page on SuperKing.

Having followed a random link I note that the piece described in the last four comments (King that can move as Queen even out of, but not through or into, check) was used in John Love-Jensen's SuperKing, posted in 1996. Therefore he seems to be its inventor (unless anyone knows of any earlier use). Whether two such pieces could face each other in that game I have yet to ascertain.
I can't fully credit you with invention of the piece you describe, because it was a discarded invention of my own. It was a transitional form of the Queen in British Chess, but it made the game trickier and more confusing. So I made the Queen less complicated by exempting QxQ from the Queen's usual movement restrictions. By the way, if you want to be accurate in the way you formally refer to me, you should call me Dr. Duniho. Mr. Duniho is my brother, but he has no interest in Chess variants.

Fair cop over 'adjacent', I do tend to concentrate on moves comprising unity and coprime leaps and neglect the rest. 'Nearest possible check' would also cover check by an Alfil, Dabbaba, or their riders, but describing check by an Alibaba or Waffle is harder. My other error is presentational. I mentioned a brilliant idea - replacing the King with something that can move long-range but not through check - gave its origin, and then considered the piece generally without the further restrictions of a particular game. This I could have made clearer. In fact I overstated the possibilities of check without the outright bare-facing ban, as check would always require the intermediate square NEAREST the checked piece to be guarded by an enemy piece. Whether what I describe is the same as Mr. Duniho's piece is a moot point, but if he wants to credit me with inventing something different I must credit him in turn for inspiring it. Either version still ranks alongside the King Battler as being stronger than the standard King but not as overwhelming as an unrestricted Kingrider.
I spotted another inaccuracy regarding the British Chess Queen. You said 'it can capture pieces checking it only if adjacent.' This does not hold for checks from the Dragon, which leaps every other space. When a Dragon checks the Queen from its closest checking position, which is two squares away, the Queen may capture it when the intervening space and the Dragon's own space are undefended.
Your comments on the Queen in British Chess, what you call a royal Kingrider, are inaccurate. A Queen may never check the other Queen. The restrictions on the Queen's movement do not hold when one Queen could attack the other. If two Queens ever did oppose each other across an empty line, which is an impossible situation in British Chess, either one could freely capture the other no matter what pieces guarded spaces in between.

It is ironic that this piece's inventor was named Modest as the latest comment by Fergus Duniho is modest indeed. Mr. Duniho has devised many of his own 'halfway Royal houses' between King and Kingrider. In Fusion Chess he has a King that can acquire extra moves by merging with Rook OR Bishop but not both, to become as powerful as Shogi's Dragon pieces. A King combined with one piece can check an uncombined King, or one combined with a different piece. Even better, in his British Chess, is a Kingrider barred not only from moving INTO check but also from moving THROUGH check, a sort of extension of en passant. Like the King Battler it can capture pieces checking it only if adjacent, and it may also find other escape routes blocked. Again the biggest difference is in the area known in Xiang Qi circles as 'facing each other bare'. If the path between these pieces is guarded by both players' other pieces there is no check, if guarded by one player's other piece(s) only that player's opponent is in check.
The advantage is that the game is less drawish than it would be with royal Kingriders. It's a prisoner's dilemma kind of advantage. There is no advantage to the player to have a King Battler rather than a Kingrider. But there is an advantage for both players when the game uses royal King Battlers instead of royal Kingriders.

What is the advantage of this piece over the simpler Kingrider, i.e., a King that always moves as a Queen? A Kingrider could still capture the piece checking it only if that piece were not protected.
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Chess Battler Advanced