I guess it would be much longer game if it did the chess thing, and it didn't allow your King to put itself into check.
It's a neat spin on the game, I dig it. I love the theme and style it has to it, and it'd be cool to see more variations to this. Like, it's already unique that it's a condensed space, everyone's right up on each other in this shrunken board, but I'd like to see it go further. Like a creative spread of duplicate pieces, a creative assembly of different maps that are in weird shapes so that you have bottlenecks, chokepoints.
Or hell, even unique pieces. Like in a map this small, knights would be OP, but their absence is really noticeable. Maybe if you did really large maps, you had a variation of knights that were like winged demons or something, so instead of a knight going two out and one beside, they had an extended range like three or four out, two or three in.
Kinda like how Advanced Wars had Artillery (Knights), but they also had Rockets (this new piece).
Also sometimes the pawns get hidden behind the tall royalty pieces, so it would be beneficial to have a look around function- I know that can be kinda limiting given the retro aesthetic of this pixel art, but even if it pulled a Doom and the sprites remained camera-facing, I think it's possible for a sequel.