There is (was) a Zillions version which grasps the game and plays it brilliantly. I lost all initial games to it... Thanks for commenting.

Why does it say stalemate is not possible? It seems the diagram of which it is claimed the best Valkyrie move is capturing the Forest Ox (Vf1xf7) actually leads directly into stalemate, through that move. After it black has no legal moves, and after hypothetical null move white cannot capture both his Kings at once, so he is not in check either. (And besides, the last black piece could have been taken elsewhere, so that neither black King would have been under attack.)

Seems clear to me. A player with only kings is forced to pass. "Checkmate" is not a thing. You just take the kings.

Vxf7 pass Vxg7 pass Kd6;-e6 1-0

But turn passing is not allowed in this game. If you read back on earlier comments to this game, one even goes so far as to state that when you can make pseudo-legal moves that would not change the board, (like using a Valkyrie's swapping move to swap it with your other Valkyrie), such a move would be illegal, because it is equivalent to a turn pass. Of course you don't even have such a move here.

In either case, since a stalemate draw cannot occur, the obvious conclusion, whether or not a king can pass, is that the side with a lone king (or 2 lone kings) loses, either by it/them being taken, or being unable to move.

I don't understand the phrase "Draws are possible; stalemates are not."  But in the addendum, point 3 is pretty clear:  

If you cannot make a move during your turn, you lose.

So the Vf1xf7 move H.G. brings up is actually a winning move.

Ah, I overlooked the addendum. So I guess what was really meant is "stalemate is a win". In fact stalemate is far more frequent here than in orthodox Chess. In the latter case the King has to be robbed of its legal moves by attacking all squares adjacent to it. Here you don't have to attack anything, as the King has no moves to begin with.

I guess you could also say that baring the King(s) is a win. But that is not the only way to get a stalemate. One or two Kings could block all moves of one, or even two Pawns.

Black to move is stalemated!

[Edit] This was very wrong; I failed to notice the Pawns also have backward moves. So I suppose the only stalemates are those where you have nothing but Kings.

The King has the simplest XBetza description of the unorthodox pieces: just xK to indicate it borrows moves from friends a K step away. The Pawn was straightforward, but gets a somewhat lengthy description, because both paths to the square two steps in front of it must be specified separately (because they bend in opposite ways).

The XBetza description of the Valkyrie uses the 'unload' operator for the moves that displace a friendly piece. There are two different kinds of such moves: a plain swap, which is specified as a simple move that unloads at the start when it captures at the end; the 'd' mode in udQ indicates friendly capture. (First-time use in a real variant!) Then there is a more complex move, that involves a third square. The diagram considers this a two-leg move with the unload square as intermediate. So you first have to click the square where the other piece is to end up, and then where the Valkyrie goes.

The Forest Ox is the worst of all. It combines a Knight move with a King-like rifle capture. XBetza cannot forge such different move types into a multi-leg move, so everything has to be reduced to a 'common denominator'. In this case everything is reduced to King steps, meaning that the initial Knight jump becomes two legs, where the intermediate square is made a don't-care w.r.t. the content of the square by allowing both moving and hopping. By using K as basic atom, each N square is reachable through two paths, but as neither is blockable that does not matter. After the first two legs for the Knight jump, two more legs follow for the rifle capture, the first making the capture as a normal capture in any possible direction, the second one to move back (cabK). Because of this description, one has to click the locust victim first, before clicking the target square of the Forest Ox.

I made a rule-enforcing Game Courier preset for Odin's Rune Chess. I chose this as a test case for the GAME code that the Play-Test Applet automatically generated, because it is notorious for having pieces with very unusual moves (causing side effects of various kinds). This makes it a good test for how such moves with side effects can be entered by means of mouse clicks. The preset can be found here.

There already was a preset for Odin't Rune Chess, but it did not enforce rules. It is still there, but now it doesn't even know the initial position, and shows the one for orthodox Chess. Last month that was different, so I don't know what happened to it.

Two modes for entering side effects

After some experimenting it became clear to me that there are two mutually incompatible ways to handle side effects with the mouse. Because mouse entry is limited to normal moves (i.e. defined by two squares, the origin and destination) and 'pass' (through the new button), but cannot be used to enter suicides or piece drops, everything has to be disguised as moves. For pieces like the Chu-Shogi Lion, which capture 'in passing' as part of a double move, the natural method is to just make the two moves: the first leg captures the piece, the second leg moves from the square where that happened to the final destination. If you want to stay at the capture square, you can pass the second move.

This way of entering moves turned out to be quite unnatural for the Forest Ox, which is described as a Knight that can make a piece adjacent to its destination disappear. This doesn't suggest the disappearence is the result of a double move, as the first move you would then have to make to get to the victim is often a very strange one (Camel or Zebra), different all the time, and how you then should get to the destination is very much dependent on where you came from. It is much more intuitive to consider the Forest Ox a Knight that can optionally make a King-like rifle capture as second move.

Something similar holds for the Valkyrie, which needs to drop a piece (the friend it just 'captured') as a side effect, rather than remove one. It also feels very unnatural to first have to move to an empty square to 'mark it for unloading', and from there perform a swap with the piece at the destination. It is much more intuitive to just capture the friend you want to displace, and then select the square where it should go to.

To accomodate that, the GAME code can be configured by defining an array shooters', containing the piece types for which side effects have to be entered after the main move. In this preset for Odin's Rune Chess this is set like

set shooters (Q q N n);

because both the Forest Ox (N) and Valkyrie (Q) fall in this class. For such pieces you always move them directly to their destination. If the move has / could have a side effect, which is not yet unambiguously defined, you will be prompted for that side effect. You can then click the just-moved piece again, to turn on highlights of the squares that could be affected by the move, and click the square where you want to apply the side effect. For a Valkyrie friendly capture this would then put the captured piece there, for a Forest Ox it would remove the clicked piece. If the side effect is optional, and the move could be made without one, you can click the Pass button.

Pieces not mentioned in the shooters array will behave as double movers, which should first be moved to the square of the side effect, and then to their destination. If the side effect is not possible on the destination of the first move (e.g. because the side effect is a capture, but the square is empty) it will be considered the final destination right away. If a side effect at the first destination is possible, but the move itself would already be pseudo-legal by ending there without side effect, the Pass button can be used to leave it at that. Otherwise you just click one of the possible final destinations, after switching on their highlights through clicking the moving piece again.

If there is a single mandatory side effect (such as when the Valkyrie captures an adjacent friendly piece; then it has to swap places with the Valkyrie), the user will not be prompted for a side effect, but the move will be auto-completed instead.