Most VPN providers don’t use DHCP. OpenVPN emulates and hooks DHCP requests client-side to hand the OS the IP it got over the OpenVPN protocol in a more standard way (unless you use Layer 2 tunnels which VPN providers don’t because it’s useless for that use case). WireGuard doesn’t support DHCP at all and it always comes from configuration.
Read this part more carefully:
By pushing routes that are more specific than a /0 CIDR range that most VPNs use, we can make routing rules that have a higher priority than the routes for the virtual interface the VPN creates.
Most traffic gets sent through a VPN only because of a default gateway (set by the VPN) in the client’s routing table. If the client’s ISP were to have their DHCP server set one or more specific routes that are broad enough to cover most of the global address space, they would effectively override that default gateway. I believe that’s the scenario described in the article.
Note that the “ISP” here could be a mobile operator, an internet cafe, an airport, someone running a wifi access point that looks like the airport’s, or a guest on the same local network running an unauthorized DHCP server.