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Gala. Daniil Frolov's incisive:

 "What's the reason of this bishop's restriction on capturing? Is it to make bishop unable to capture adjecent pawn (since rook is often reattaked when attacks adjecent pawn from central zone to castle, while bishop could attack pawn from unconvenient point)? Or it's artifact of some imitating of real-life warriors? Or what?"

There may be historical subvariants of Gala, and there are other German sources to resolve ambiguities. But I think other commenter Mayer, Frolov and myself have agreed-on standard Rules in mind by now.  Solvable pint-size Shatranj on 64 squares and her step-daughter Simpleminded Chess on pint-size 64 -- become our f.i.d.e. OrthoChess -- did survive or emerge out of the Middle Ages.  More substantial and challenging Gala on 10x10 as well as heterodox 12th-century Courier-Spiel on 8x12 are less known.  

Gala's King is our same King except chiefly for taking only over Wall -- that qualifies Him for variantists' "divergent."  Korna (Rook) moves Bishop-like within interior 32 squares exclusive of the 4 holy centre squares.  Horsa (Bishop) moves Rook-like those 32 squares.  Therefore, each Korna and Horsa switches mode upon having crossed any Wall, otherwise called deflection line.  (Gala's only 4 piece-types do without Knight/Horse, perhaps unknown to "barbarians."  As custom, instead of "Check," one says "Gala" same context.)

Thus Korna and Horsa readily admit serial Rook and Bishop direction, and vice versa, in one single move.  That occasioned change of direction is like 13th-century Grande Acedrej Gryphon, http://www.chessvariants.org/historic.dir/acedrex.html, and also like modern fixed-length multi-path Falcon, http://www.chessvariants.org/large.dir/falcon.html.

Now Frolov's "why the Horsa/Bishop capture prohibition across Wall" has two remarkable explanations: (1) Nod to full Bishop's inability, as in Courier-Spiel http://www.chessvariants.org/historic.dir/courier.html,  to reach half the squares when board is unpartitioned, and so appropriate restriction; (2) Opposition to King method of capturing only across Wall, a perfect counterbalance!  It's as if futuristic, ancient Gala wants to collapse into just one piece-type from its four, once the utility Kampas(Pawns) are factored in; for they do have both orthogonal and diagonal mobility according to position too.  

Though the World went another way and Gala is doomed to stay exotic, isn't even this regionaliziing of the board also more basic than Simpleminded f.i.d.e. OrthoChess on little homogeneous 64 squares?