Well, there is clearly a motor and a battery, hence the bulked up downtube and the unit on the backside of the seat tube. That's what makes it an e-bike
I guess I differ from you in that I support having non-motorized places to go, where you can ride a human powered bike. As for "foot only", the closest you'll get is Wilderness which bans all forms of mechanized travel and is only open to horses and foot traffic, but that's a whole other topic....
Personally, I would be happy to see some places not open to horses, where you have no choice but to walk as you said.