Perhaps it is easier to understand by taking an actual example? Suppose we simplify XQ and Chess such that there are only white pieces, and only 2 Rooks and a King. Chess would have 64*63*62/2 = 124,992 different board positions without castling rights, 62 with only K-side or Q-side rights, and 1 where you have both rights. Not all positions represent different game states, however: for every position without castling rights (say Kg3, Rb2, Re7) there exists an equivalent one that is its mirror image (in the mentioned case Kb3, Rg2, Rd7). This mirror image is never equal to itself, as a piece always moves to another square on reflection, the number of file being even. The two mirror images represent the same game state. So the number of game states is only 62,496 + 2*62 + 1 = 62621.
For Xiangqi there are 9*89*88/2 = 35,244 positions. Of these, 3*40 are symmetric (K on e0, e1 or e2, one Rook in the rectangle a0-d0-d9-a9, and the other Rook in the mirror position, i.e. on f6 if the other was on d6 etc.). All the other positions are asymmetric, (e.g. Kf1, Rb2, Rg7), and transform into a different position when mirrored in the central file (Kd1, Rh2, Rg7 in the mentioned case). These two positions are equivalent,and together represent one game state. So there are (35,244 - 120)/2 + 120 = 17,682 game states.
You see that the division by 2 of the number of positions to get game states occurs both on 8x8 and on 9x10. In XQ there are 60 extra game states compared to a simple dicvision by 2 (0.34%) because of the symmetric positions possible on an odd-width board. Quite negligible. For Chess there were 125 extra positions (0.2%) because of castling.
The lower XQ number is caused by the King confinement. Evenness of the board width hardly enters.
You seem to be fixated on positions that can be reached in just a few moves from the standard opening position. These form a totally negligible fraction of all positions. 'Game-state complexity' refers to all reachable positions, not to the positions that happen to occur frequently in GM games. Actually positions with a King on b1 (which are the mirror image of positions with a King on g1) are not nearly as uncommon as you seem to suggest. There is no magic involved at all in reaching them. Just Q-side castling...
You are confusing non-equivalence of mirrored moves in positions where the symmetry is already broken with absence of symmetry. f4 is exactly the same for positions where the King stands on d1 as c4 is in the more common position where the King is on e1 (if the Rooks have already moved). That the symmetric partners of Chess positions are all rarely encountered in games, because people do not like to destroy their castling rights by putting the King on d1, is totally irrelevant for how many positions there exist.
In XQ playing Cb2-b9 is also totally different from playing Ch2-h9, after black has played Af9-e8.