The case can send battery-status info to the iPhone when the lid is flipped open and held within a few inches of the phone — more than a few inches and it doesn't work. This sending status seems to work even if BlueTooth & Wi-FI are turned off. All this taken together seems to indicate it’s using NFC for this function. Know the iPhone has NFC (it’s used for ApplePay).
Does the W1 chip have imbedded NFC ?