[nurettin]

As I remember, when you step slowly from the middle of a tile, you always end up on the edge of that tile. And if there is a chasm and you try to step once again, you almost trip and regain balance. If there is no chasm, you step to the middle of the next tile.

[teddyh]

IIRC, you can adjust your position quite precisely by crouching, which has a side effect of making you move forward a tiny little bit. Yes, stepping towards a chasm will make you stop at the edge, but that does not alter the fact that your position is definitely not clipped to fixed steps, as the article erroneously claims.