Language is fluid and words change meaning.
Over here moped also originated in motor + pedal, but now just refers to twist and go type scooters and in fact is used in the
legal definition in preference to motor scooter.
E-bike (ebike, eBike, electric bike) is a word that is now being widely used for anything with 2 wheels and an electric motor that you sit on. If people are using it to mean that, that's what the word now means. There's no changing that now, the cat's bolted from the stable and the horse is out of the bag.
Legally here we have "EAPC" - electric assisted pedal cycle, motor up to 250w continuous power, motor only operates while the pedals are turning and up to 25 km/h, no throttle except for "walk assist. EAPCs are legally considered a bicycle except you need to be 14 to ride one.
Any electric two wheeler that doesn't comply with the above is legally either a "moped" or an electric motorcycle depending on power.
The article in the OP seems to be just talking about restrictions on the "class 3" bikes, which seems reasonable to me.