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Now, now, I did specify a 'completely empty 3x3 block of non-Tardis cells' - although I have now highlighted it in response.

This is a really interesting idea!

The Fortress that is bigger on the inside is a good stand-alone idea; allowing it to move really changes things.  I wonder how easy it is to move the tardis and achieve instant checkmate?

One suggestion: shouldn't the main board, instead of being H-shaped, be a rectangle?  At the start of the game, 9x2 squares would be covered by the two tardises--functionally the same as your setup.  However, when a tardis moves, there would still be squares where the tardis started.  It makes more sense to me.

A piece moving diagonally through a cell orthogonally adjacent to a Tardis may do so through either two opposite corners of that cell, or one of the non-Tardis corners and halfway along the Tardis-bordering edge.

It took me disappointingly long to figure out how said diagonal moves into/out of the Tardises work, but I think I've got it now: for reference, a bishop starting from c4 could move souteast into the white Tardis (in its starting position as shown in the diagram) and continue along its a6–f1 diagonal; from d4 it could go southeast b6–f2 or c6–f3, able in both cases to exit to the main board's g1; from e4 the southeast move takes it either d6–f4 or e6–f5, exiting onto g2; and moving southeast from f4 it may reach g3 via the Tardis' f6 or skip that square completely. Ofc from the latter three squares there are southwestward Tardis‐crossing moves too, and likewise from other squares.

a player may move the entire Tardis […] to swap place with any completely empty 3x3 block of non-Tardis cells

I see where this comes from, though it seems the emphasised restricion may be unnecessary at least in theory; the path‐splitting rule seems like it could be unambiguously be applied recursively, and from a lore perspective Tardises (well, the TARDIS) have been known to materialise inside each other (or even inside themselves, whether at the same or different points in their own timeline) on the show. The only problematic case would be a Tardis straddling a Tardis' edge (though they've never been seen inside each other's doors either, so…).

Subdividing the original Xiang Qi board

It seems the array diagram is missing a rank :‌(

For what it's worth, I like the idea behind this game a lot, though I haven't had a chance to try it; the unusual connectivity is interesting, the moving palaces a nice addition, and the way of incorporating extra space innovative. And the Tardis is the last entry in Man and Beast, too; a suitably unusual way to finish an epic series of articles.

This concept of Tardises is very nice, but I am a bit worried that when they can be used to teleport Kings, achieving checkmate would be a hopeless task. The way they are implemented here In this particular incarnation they are also a bit large for my taste. I would be inclined to make them 2x2 on the outside, and 4x4 on the inside (embedded in an 8x8 board). And have the additional rule that it would not be allowed to move a Tardis when in check. An even more modest implementation would be a single square, and internally 2x2. This has the advantage that every square in it still borders the outside world, so that a King in there can still be easily checked.

I've thought of smaller tardises before too, and agree that for most games they'd probably be more practical. As for checkmating difficulty, it seems that Charles was probably relying on the fact that Kings are confined to them, and so presumably the idea (or at least one possible strat) is to get as many offensive forces inside the tardises as possible while the board is still full enough to prevent too much tardis movement (as in the opening setup) and then use that to attack where the king can't escape. And potentially keep the armies spread‐out enough to prevent too much possible movement.

I agree that stopping teleportation whilst in check (after all, The Doctor sticks around until the danger's gone…) looks like a viable option should this indeed be unwinnable in practice