'Balance' isn't a style, it's a way to let various styles interact in the same game without wrecking it - balance is not one of the conflicting goals that must reach a compromise, balance /is/ the compromise.
I would think in this case, "balance" refers to the "all options roughly equal" style of character/monster building necessary to grade challenges, which is important for Gamist play. Balance between, say, combat and exploration is a different issue.
Just for interest, here is some discussion from
Ron Edwards on balance:
"Balance" is one of those words which is applied to a wide variety of activities or practices that may be independent or even contradictory. . . . The word is thrown about like a shuttlecock with little reference to any definition at all. That's the current state of the art. So I'm taking time-out . . . to go on a full GNS balance rant, because the assumption that Gamist play is uniquely or definitively concerned with "balance" is very, very mistaken.
Overall
1.Compare "balance" with the notion of parity, or equality of performance or resources. If a game includes enforced parity, is it is balanced? Is it that simple? And if not, then what?
2.Bear in mind that Fairness and Parity are not synonymous. One or the other might be the real priority regardless of which word is being used. Also, "Fair" generally means, "What I want."
3.Are we discussing the totality of a character (Effectiveness, Resource, Metagame), or are we discussing Effectiveness only, or Effectiveness + Resource only?
4.Are we discussing "screen time" for characters at all, which has nothing to do with their abilities/oomph?
5.Are we discussing anything to do at all with players, or rather, with the people at the table? Can we talk about balance in regard to attention, respect, and input among them? Does it have anything to do with Balance of Power, referring to how "the buck" (where it stops) is distributed among the members of the group?
They can't all be balance at once.
Within Gamist play
1.Parity of starting point, with free rein given to differing degrees of improvement after that. Basically, this means that "we all start equal" but after that, anything goes, and if A gets better than B, then that's fine.
2.The relative Effectiveness of different categories of strategy: magic vs. physical combat, for instance, or pumping more investment into quickness rather than endurance. In this sense, "balance" means that any strategy is at least potentially effective, and "unbalanced" means numerically broken.
3.Related to #2, a team that is not equipped for the expected range of potential dangers is sometimes called unbalanced.
4.In direct contrast to #1, "balance" can also mean that everyone is subject to the same vagaries of fate (Fortune). That is, play is "balanced" if everyone has a chance to save against the Killer Death Trap. Or it's balanced because we all rolled 3d6 for Strength, regardless of what everyone individually ended up with. (Tunnels & Trolls is all about this kind of play.)
5.The resistance of a game to deliberate Breaking.
Within Simulationist play
I am forced to speak historically here, in reference to existing and widespread Simulationist approaches, not to any potential or theoretical ones. So think of Call of Cthulhu, GURPS, and Rolemaster as you read the next part.
1.One fascinating way that the term is applied is to the Currency-based relationship among the components of a character: Effectiveness, Resource, Metagame. That's right - we're not talking about balance among characters at all, but rather balance within the interacting components of a single character. I realize that this sounds weird. Check back in the Sim essay to see how important these within-character interactions can be in this mode of play.
2.And, completely differently, "balance" is often invoked as an anti-Gamist play defense, specifically in terms of not permitting characters to change very much relative to one another, as all of them improve. This is, I think, the origin of "everyone gets a couple EPs at the end of each session" approach, as opposed to "everyone gets different EPs on the basis of individual performance."
3.Rules-enforcement in terms of Effectiveness, which is why GURPS has point-total limits per setting. Note that heavy layering renders this very vulnerable to Gamist Drift.
Within Narrativist play
This gets a little tricky because I can't think of a single coherent Narrativist game text in which balance as a term is invoked as a design or play feature, nor any particular instance of play I've been involved in which brought the issue up. But I'm pretty sure that it's a protagonism issue.
1."Balance" might be relevant as a measure of character screen time, or perhaps weight of screen time rather than absolute length. This is not solely the effectiveness-issue which confuses everyone. Comics fans will recognize that Hawkeye is just as significant as Thor, as a member of the Avengers, or even more so. In game terms, this is a Character Components issue: Hawkeye would have a high Metagame component whereas Thor would have a higher Effectiveness component.
2.Balance of Power is relevant to all forms of play, but it strikes me as especially testy in this mode.
That's the end of my balance rant, but I beg and plead of anyone who reads this essay: I would very much like never to hear again that (1) Gamist play must be uniquely obsessed with balance, or (2) if play is concerned with any form of balance, it must be Gamist. These are unsupportable habits of thought that pervade our hobby and represent very poor understanding of the issues involved.
Lewis Pulsipher also has coments on balance, from a companion article to the one quoted in the OP. I don't have it ready-to-hand, so I'll summarise: he notes that MUs are the most powerful and versatile PCs at mid and high levels, and suggests that GMs will have to be careful to avoid having the players of MUs dominate play.
This could be seen as an instance of Edwards' Gamist 2 (effectiveness of different strategies), and at the extreme 5 (breaking), Simulationist 3 (character effectiveness that extends beyond the notional level-appropriate limits) and Narrativist 1 (players of wizards get disproportionate screen time). Obviously some players (including, perhaps, Gygax) think that the power trajectory for MUs is an instance of balance in the sense of Gamist 2, but with a longer real-world conception of the unit of play over which effectiveness of strategies must be balanced: fighters are more viable at the start but have a power cap; MUs are vulnerable at start but lack the same cap. (This obviously won't work if players are allowed to start characters above 1st or 2nd level.)
4e, with its martial encounter and daily powers, can be seen as a version of Edwards' Thor vs Hawkeye point: fighters get meta-resources to balance the raw effectiveness of mages. But obviously this is controversial. One balance-style criticism I have seen is a version of Edwards' Simulationist 1 - namely, that it's unfair that fighter players get all this "meta" as part of their build when mage players don't.
Which I think is consistent with the point that not all these forms of balance can be achieved simultaneously.