No, they are not floating, yet this author uses this word to describe chinampas.
Anyway, as a side note, I would say that a “modern” technology that somewhat mimics this is aquaponics. This method can be very powerful as it feeds off stacking biodiversity, just like the chinampas.
Your aquaponics analogy is apt. The canals are periodically dredged for fish manure in addition to some fish and axolotl (salamander) harvesting. Compare the Incan soku kollu technique, which starts with land and digs irrigation canals close together in which fish such as talapia are raised and harvested. The water serves as thermal mass and the mist they emit during frost events protects the plants.