It sounds to me like you are looking for Hillfolk - or rather, the DramaSystem found in the book of the same name. Let me give you the quick rundown:
- Robin D. Laws spent a long time studying stories and presented a new system for describing story interactions in his book, Hamlet's Hit Points
- He then created a game based on that research, one that instead of trying to model, for instance, muscle-powered melee combat, tried to model the story interactions described in HHP. That game is Hillfolk.
- The system that powers Hillfolk is the DramaSystem. It's in the same book as the Hillfolk setting, along with a bunch of other settings ("series pitches" in the game's parlance).
This is the best game I know of for your needs - but even it doesn't match perfectly. Let's take a look at your requirements and see where it works and where it doesn't:
- Allows for freeform (for the most part) play -- and isn't terribly genre-dependent (i.e. doesn't assume things about what NPCs will be like, what races exist in the world, what the world looks like, etal)
Even the main book has 30 additional settings for the game. It is officially recommended that you try the base setting (Iron Age raiders in the Levant) first, because it puts the focus on dramatic interactions instead of the use of magic, powers, or violence. It assumes only that your game will have characters created according to the rules.
In my experience, if your players are not interested in the base setting it is a waste of time and frankly counter-productive to start with that. Player investment trumps so much else.
- Supports player vs. player conflict fully
Hillfolk is about player vs. player conflict - dramatic conflict. The key here is that the game is designed to create play that is similar to modern serial TV dramas. Dramatic conflict is about what characters want from each other and why they can't have it. Go watch basically any good dramatic TV show from Buffy or The Sopranos onward and you'll see it in action. The game makes these scenes the core of the game, and systematizes their resolution.
- Provides an arbitration system of "last resort" as a tiebreaker -- outside the control of the participants, that is. Dice are acceptable for this task -- in a digital environment, a roller can be assumed.
The game provides a procedural resolution mechanic, too, though it is far from integral to the game and any mechanic you wanted could be lifted from another game and used instead. But there is no tiebreaker for dramatic conflicts - and no need for one. The flow of drama points in the game means that each player always has a reason to concede (instead of just digging in) or that one player can force things to go his way.
- GMless or GM-optional play -- the need to have a GM come in from 'outside' the situation at hand and be an arbiter would simply be too difficult for a 'last resort' mechanism
This is one area where Hillfolk doesn't quite deliver. It assumes a GM. However, the GM role is already minimized. GMs call the initial scene, but all players will call scenes in the course of the game, following stories or switching focus as they want. GMs are also there to help decide when a scene is over and a decision has to be made, but this is something that could be devolved to the group, too. GMs also play the opposition and all NPCs. Again, your group could distribute that responsibility if they like.
- Can be played in a digital environment (chat+roller minimum) -- in person play is largely infeasible for me due to transit issues
Hillfolk needs very little in the way of props. The main requirement is for keeping track of drama points - and while in person you might just pass tokens around, it's not hard to just keep track of them on paper or in a shared document online instead. The procedural system requires a deck of cards and some more tokens, but you can substitute another system. In practice, procedural tests wither away as your group concentrates on the dramatic meat.
- Suitable for small group (2-5) play, or small subgroups within a larger group that uses the system
Again, the smallest groups might be a challenge. I think you'd need 3 to be reasonable, (2 players & GM), up to about 6. If you're going GM-less, then possibly you could make it work with 2? In a game about dramatic conflict, you have to have 3 to make a basic triangle or things just go back-and-forth like ping-pong and it gets stale. Maybe multiple PCs per player could solve this problem?
- Finally -- it needs to be reasonably accessible (i.e. I don't have to wade through 5000 pages of material just to get the basics of the system down) if not minimalistic
The core of the dramatic resolution system is on 3 pages. You could email a 1/2 page summary to your players.
For more information on Hillfolk, check out some other questions and answers here and of course, the official site linked in the headline above.