Resolving Tactical Combat without Maps
I run mapless combat here with 4th Edition. It works fairly well, but it's not perfect.
What I find is that it's not enough to let description speak for itself. If I move or position a figure on a battlemat, it's easy to see if I provoke opportunity attacks, or what size area attack could hit both this figure and this other one but not that other one. If everyone just speaks in rough terms it might not be clear what a given maneuver achieves. Even if they give exact relative distances from every other figure or feature (which I hope they don't do), synergies that might be visible on a map might not be apparent to anyone.
So, I focus on and I ask my players to focus on what they're trying to achieve with their movement. It might be several things like "get out of flanking and behind cover" or "get close enough to my ally for healing word but far enough away that we can't both be hit by the flameskull's fireball."
I find that this works because I find that in the vast majority of cases, if there isn't something specifically preventing or triggering off of a movement or position, then it's possible to achieve. Sometimes finding the exact way in which it can be achieved takes a bunch of people sitting around a table counting, sketching, referencing rules and arguing more than they're actually playing, but the point is that there's a way.
So, if I just assume there's a way to do something that no one has specifically said can't be done, and if I game with people who want every one to be having fun rather than annoyed and miserable, it works pretty well.