After watching these two videos carefully, my analysis is as such:
Presenter 1 used the term smartphone colloquially. He did not really know what he was committing to by suggesting that.
Presenter 2 was knowledgeable of the device. He revealed that the watch is only unlocking the car with NFC (proximity tech, not radio TX) but that eventually Bluetooth technology would be implemented. The app to be used on smartphone or that tablet was the account management app for the Audi security feature in the car's computer. It most likely communicates over the web with the computer in the car, not the watch.
In other vids, the watch appeared to be using cellular data only at this time as it displayed T-Mobile H+. There was no Wi-Fi or BT icons lit. I could not find evidence to support phone service either. It does display the NFC icon. So there's a ways to go. It's very possible they only brought it to offset the hype for Hyundai's device. They possibly were not even expecting interest in the OS of the device to be so great.
I would not expect the watch to communicate the vehicle security functions over the web, it's an obvious point of vulnerability. The cars computer would be the hub. But that could be android. The devices would communicate over BT. I'm sure they are working on securing this now.
The phone you pictured, it sounded like he was suggesting the mobile app which was on watch, could also be installed on a phone and given permission. Of course this device would only have the BT function if it did not have NFC proximity technology like a key fob would.
The other big reveal here: Inductive charging dock in the car! For the watch? Excellent!