Zigbee devices don't have internet access because they're not on the network. Zigbee is a seperate wireless protocol. Lights and switches implement a pairing step which allows them to interact. If you would like to control such devices from your PC, you'll need a device with a Zigbee transceiver to talk to these devices.

Typically, manufacturers sell you a "bridge" or "gateway", which is a networked device including such a transceiver. You could isolate this single device from accessing the internet or you could just not rely on any closed option. You can buy a USB Zigbee transceiver for 30 EUR and use it with your PC or a Raspberry Pi.