Simple Q&A D&D 3.5 (by RAW) XXI

[Andezzar]

But a monk's unarmed strike counts as a weapon,

No:

A monk’s unarmed strike is treated both as a manufactured weapon and a natural weapon for the purpose of spells and effects that enhance or improve either manufactured weapons or natural weapons.

and so he gets the same effect from Flurry of Blows that he would get if he used the Two-Weapon Fighting action to make two unarmed strike attacks (both of which would get his full STRMOD) and had the TWF feat to reduce the penalties to -2/-2.

You can't make two attacks with an unarmed strike unless you get iteratives or use Flurry of Blows.

Other characters can't duplicate this feat with their unarmed strikes because they're not monks, but the only thing that's unique to the monk in this scenario is the way his unarmed strike works; if a DM-created light weapon dealt 1d6 lethal or nonlethal bludgeoning and always added your STR bonus regardless of handedness, a character wielding two such weapons would function exactly like a monk doing two unarmed strikes (except that the monk could be kicking instead of punching while holding a mahogany armoire in his hands).

Even if it works similarly or exactly in the same way, it does not mean that it is the same thing.