How to use Wake On Demand?
Both lines are correct. You WiFi card supports Wake-On-Lan (WOL) but the link across it does not.

It's almost impossible to get WOL working across a net of any size as it relies on sending and receiving broadcast UDP packets on port 7 or 9 and broadcast packets are rarely routed.

To get it working you would need to reconfigure your home router and set up a VPN between the router and the device you want to send the WOL packet.