Maybe I'm missing something important. Is this purely an overlay network on top of regular IP with regular ISPs? Or have the got their own physical layer that I missed during reading? My confusion comes from LAN usually implying physical layer colocation. Otherwise, wouldn't it be a WAN?

The network is made up of independently operated and heterogeneous nodes (currently three nodes, a mix of Debian using strongSwan and OpenBSD using iked), which peer over IPSec links.

It's a VPN connecting sites together to form something like a LAN, but geographically separated. Multinational company "LAN"s are set up in a similar fashion.