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That just sounds like "side-to-side" to me.
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Right side, left side, front side, back side, side-to-side 
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A "lateral" pass in (American) football goes across the width of the field; it doesn't move the ball down the length of the field (or not much anyway).
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As opposed to longitudinal?
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Lateral encapsulates longitudinal
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How about "Axially (in 2D)" or "Tranverso-Longitudinally"? 
You have just been Sharapova'd.
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That doesn't sound right either; that seems more like "corner-to-corner".
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PIEBALDconsult wrote: That doesn't sound right either; that seems more like "corner-to-corner".
No, "axially" means "along" an axis. So in 2D, it's either along X (left-right) or Y (forward-backward) - assuming the rook at (0,0). It doesn't have to be corner-to-corner.
The other term I mentioned is related to anatomy and is also correct, although it's not a proper word. (ref[^])
You have just been Sharapova'd.
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But if I had to draw axes on a chess board, I'd draw them diagonally. These are the only bisecting lines a chess piece may travel.
"Transverse" might suffice for my purpose, but I was hoping for a more widely used term.
I see "crossing from side to side; athwart; crossways" and "at right angles to the long axis" (a chess board has no long axis of course).
So I'll use "transversely" for now; no one will see it but me anyway. 
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PIEBALDconsult wrote: But if I had to draw axes on a chess board, I'd draw them diagonally.
That seems odd. Perhaps you're swayed by the alternating colors of the squares and like most people, notice that the diagonals stand out more?
/ravi
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I'm surprised no one said "rookfully" 
<sig notetoself="think of a better signature">
<first>Jim</first> <last>Meadors</last>
</sig>
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"rookfully"
Bad command or file name. Bad, bad command! Sit! Stay! Staaaay...
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"orthogonally" ?
I know there is a question of "orthogonal to what", but I think it's pretty intuitive.
Cheers,
Peter
Software rusts. Simon Stephenson, ca 1994. So does this signature. me, 2012
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The bishop as well as the rook move orthoganally, if you look at the two possible moves they can make.
Ok, it really depends on the chess board having square fields, but that is mostly the case or at least close enough to square not to make a difference.
Cheers!
"I had the right to remain silent, but I didn't have the ability!"
Ron White, Comedian
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"Orthogonally" was my first thought. So I have ploughed through the responses to see if anyone else had the same idea.
Wise men always agree and fools seldom differ.
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Easy...
Go back to castle. Everybody knows castles don't move. Voila - problem solved! 
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Of the available antonyms offered for diagonally by your run of the mill thesausrus I think perpendicular is pretty much spot on.
Considering you didn't have any problems with diagonally for the bishops move. Diagonally here is obviously in relation to the rectangular sides of the board and the same can be applies to perpendicular movement.
"Side-to-side for any two parallel sides of the board" wouldn't be an option I guess, too worday!
(The fact that each of these pairs of moves is in itself arranged in an orthogonal fashion is only attributed to the fact that most of the time the fields of a chess board are square.)
Cheers!
"I had the right to remain silent, but I didn't have the ability!"
Ron White, Comedian
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Good luck with the Knight then
GCS d--- s-/++ a- C++++ U+++ P- L- E-- W++ N++ o+ K- w+++ O? M-- V? PS+ PE- Y+ PGP t++ 5? X R++ tv-- b+ DI+++ D++ G e++>+++ h--- ++>+++ y+++* Weapons extension: ma- k++ F+2 X
If you think 'goto' is evil, try writing an Assembly program without JMP. -- TNCaver
"When you have eliminated the JavaScript, whatever remains must be an empty page." -- Mike Hankey
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Knight == "special". 
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PIEBALDconsult wrote: Is there a generally accepted one-word description of how a rook moves?
No!
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I thought not. Alas. 
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Squarely?
There are two types of people in this world: those that pronounce GIF with a soft G, and those who do not deserve to speak words, ever.
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Hello!
I'm working on an article on ASP.NET 5 with AngularJS2 and Typescript, using Visual Studio. Planning to be publishing it this Sunday.
Good to be back in the game 
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