The way the result is obtained is generic and could be generalized to bigger chess settings or to other games.
I am not fully in agreement with this assertion. It seems that the 5x5 game tends to trade off the pawns too fast. Furthermore, White has no "blitz" win (such as aiming for the enemy King), so if down a pawn after a few moves, White has no hope (even with equal material Black typically draws). The authors themselves note something along these lines (paragraph 4 of section 2):
It turns out that most of the deviations from the main line can be quickly decided. It is mainly due to the fact that in Gardner’s chess pawns are immediately exchanged or blocked. Moreover, pieces cannot develop naturally since almost all free squares are controlled by pawns. Also the fact that promotion happens quickly leads to some very rapid checkmates that allow to prune the game tree.
In particular, if White opens by pushing the knight pawn this loses a pawn (rook file pin), while pushing the rook pawn leads to a pawn then piece exchange (if White does not recapture the pawn is lost) and the dust quickly settles. Similarly with the king pawn push.
For the B and Q pawn pushes, Black aims to blockade. One aspect of the current setup is that (particularly) after a push of the rook pawn [by either side], the knight's movement can be suppressed by pawn guards, and the bishop is similarly clunky [especially when the opponent has a pawn on the central square]. So White has to exchange pawns early, and as with the other lines, this kills all tension.
On a larger board (5x6 even), I don't think there is such an early detonation. Maybe even some of the others in the 5x5 class (varying RNBQK, perhaps asymmetrically) could be more interesting (the authors do not discuss this).