IMO the text is pretty clear: "monk weapons" are defined as shortswords and simple melee weapons without two-handed or heavy properties. Full stop. This does not include darts. Monks are proficient with darts, but that does not make them a "monk weapon".
That said, daggers definitely are monk weapons, and when thrown are pretty much mechanically identical to darts, so I don't really think it matters very much. Technically by RAW, if a monk throws a dart they don't get the bonus action unarmed attack, whereas they could if they threw a dagger, and the dart damage won't scale with level (but this only matters after level 5). But either version still allows for Flurry, Extra Attack, etc...