The question has already been answered in the other thread.

Squares and not hexes because Brad Wardell doesn't like hexes.

Bees don't like Brad.

I agree this game should be made of hexes, the fact that Brad doesn't like\know wargames IMO is one of the main reasons this game has problems: movement is incoherent and buggy (0 movement points coming out of cities?, using auto fight spends one movement point fighting manually a boring battle makes you save that movement point?) battles are slow... etc...

But Brad is also a smart, committed guy. Hopefully he will change his mind in the future and\or will find all necessary fixes.

Somethings are fixable, others aren't. The square tiles is too central in the game design to switch out like it was nothing, all the tilesets would have to be redone. Asking about this now is like 2 years way too late.

Because chess would totally be a better strategic game if it was played on a hexagonal board.

I really don't understand the love of hexes.  It's a slightly different shape that works out to function the same as a staggered grid.  If you take Elemental's grid and shift every other row 1/2 a square to the right you would have the identical system it just wouldn't look as "pretty."  With a grid each square has 8 adjacent squares.  With a hex system or a staggered grid each square has 6 adjacent squares, and that's the end of the functional difference.

Hex maps are more nuetral and harder to exploit distances than square tile maps but if the head-guy does not like hexes, then that's that.  Live with squares. 

But please fix the Kingdom Tech Tree.

Would it help if we called the squares tetragons?

It's easier for devs and modders to work with right angles and squares don't have any real disadvantage if diagonal movement counts as 1.4 moves.
This game has floats and not just integers. What's the problem?

Does Diagonal movement count as 1.4 moves?  I understand your point however I think that you highlight the problem with your IF above.  You're kind of a bright fellow not to notice this game does not do this..

Squares can be easily linked to a matrix. And that is easily understandable by an AI.

Not sure you understand what today's AI is capable of (or not cabale of) if you think AI can understand a matrix.  If you mean a  square matrix is a simpler construct/logic to program into the AI than a Hex matrix then you are only on the right track. However if you think of a Hex matrix as a matrix itself but each element is a circle with 6 sides each with 60 degree arcs.  A Square matrix is the same but owith only 4 sides and 90 Degree arcs.  In this way of thinking about them they are the same and if diagonal movement was 1.4x the cost of adjacent movement then they would be equivilent as Robert pointed out above.

Because it's possibly the finest turn-based strategy game ever created and gets along just fine with a square grid.

More to the point, a hexagonal grid is not inherently superior.

That's purely aesthetic.  Units don't gain an advantage by moving diagonally.