To my untrained eye, the "camera" is looking at the characters in question mainly from the side. You're seeing what would be the front of the bodies (the chest) because they are standing in a combat-ready pose (as you posited) that is akin to a fencer's pose (to help minimize the surface area presented to the foe).
Not all of the characters have as much tilt to their body, which accounts for some of the variation.
I don't think the actual "camera" is viewing the characters on a diagonal, like in your last sketch, because if you were to draw a horizontal line at the level of each sprite's heels you'd see the heel of both feet is generally on or quite near that line (unlike in your last sketch). Though the bottom pixel of the "back" feet is often lower than that of the front, that's due to perspective and the fact that the character's feet are at approximate right angles to eachother.