Unfortunately, this mess basically has no resolution, and touches upon several other messes which also have no resolution.
The first and foremost thing about this is that “off-hand” is an extremely weird concept in D&D 3.5e. If you aren’t using two-weapon fighting, you don’t have one. The term is never defined—and rarely used—outside of two-weapon fighting, and even there its “definition” is implicit. Two-weapon fighting defines a few things about your off-hand—how it affects your two-weapon fighting penalties, how much of your Strength bonus you can apply to damage with it, and so on—but it doesn’t really define “off-hand” itself.
The second is that two-weapon fighting and unarmed strikes is extremely ill-defined. The rules for two-weapon fighting require that you have “a second weapon” “in your off-hand,” and both of those terms are problematic.
For one, unarmed strike is defined as a “weapon” that covers hitting with any part of your body. All strikes with body parts use the same unarmed strike “weapon.” Therefore, it’s very unclear whether or not you can use two-weapon fighting with unarmed strikes alone—because striking with one part of your body and then striking with another part—e.g. each fist—counts as using the same “weapon” twice, not using two different ones. Neither is “a second weapon.”
On top of that, “in your off-hand” is a problem because your unarmed strike isn’t in any hand—and may in fact not actually use a hand, since it could be a kick or a headbutt or whatever. So it’s arguable that—despite explicitly being a “light weapon” for the purposes of two-weapon fighting—an unarmed strike cannot be “in your off-hand” as two-weapon fighting requires.
And we haven’t even gotten to the monk yet. All of the above applies to every character.
Then we get to the monk “feature” quoted in the question, that there is no such thing as “off-hand” for a monk’s unarmed strikes. Outside of two-weapon fighting, this is true for everyone else, as well, and per the above, inside of two-weapon fighting, we already had significant problems with the possibility of an off-hand unarmed strike. Taken literally, though, this monk “feature” really cements the inability to combine the two for the class most likely to want to do it.
Even then, though, we can’t even say something like “yeah, RAW doesn’t suppose unarmed strikes when two-weapon fighting, RAW is dumb, just houserule it,” like we do for a monk’s lack of unarmed strike proficiency. Cuz it definitely isn’t clear RAW that you can’t use an unarmed strike in two-weapon fighting, as a monk or otherwise. Stuff like the authors’ apparent need to say something about the monk’s unarmed strike vis a vis off-hand, the reference to unarmed strikes as light weapons, and so on, all build up RAW actually allowing it, contradicting itself. RAW clearly does want to allow unarmed strikes while two-weapon fighting, it’s just… broken, I guess, on actually describing it. So there’s no resolution here, not even a dumb one.
I think it’s pretty likely that all the authors really meant is that all of the downsides of being off-hand don’t apply to a monk’s unarmed strikes. The quoted line appears immediately prior to a line explicitly stating the halved Strength bonus to damage doesn’t apply, for instance, which is the main drawback of an off-hand attack. It seems to me that the authors simply wanted to cover any other downsides of an off-hand attack, whether from the core rules or from the particular features of a given class, feat, or whatever—including those that hadn’t been written yet.
But ultimately, that’s a guess. The mess that we have is evidence for it, as are some of the things stated in the Rules of the Game articles on Wizards’ website and some of the answers given in the FAQ, but ultimately all of that evidence is only evidence, not proof.
The other possibility I can imagine is that the authors never imagined a monk would ever want to use two-weapon fighting, since flurry of blows already “covered” that. Sort of. Except that, RAW at least, you definitely can combine the two, and that is kind of a significant option (or would be if the monk had any decent way of achieving the requisite accuracy to pull that off). And in any event, this is part of the unarmed strike feature, not the flurry of blows feature, which really shouldn’t have been written assuming flurry of blows since they aren’t the same thing. Still, could be worse—we could have Paizo’s “flurry of blows is two-weapon fighting” fiasco, like Pathfinder.