I think the keyword is "over IP". My understanding is that Zigbee works at the lower layers.
Zigbee is not IP. It's a completely different network, which is why many Zigbee based solutions often require a hub/gateway (which speaks both IP and Zigbee) to enable control via smart-phone apps or stuff like that.
To be honest, I'm pretty happy about that. The less my smart-devices has to do with my local wifi/LAN, the happier I am.
Not really sure I like the direction this is heading.
In that regard I much prefer non-IP based devices.