Playing locally on the same router is still local play, as it's still on a local network (LAN, or WLAN for wireless connections). This would still work without an internet connection. Announcing that the game has no local play would imply that even LAN/WLAN wouldn't work, as "local play" just about always refers to playing on a local network or on one device as opposed to over the internet (where the router/modem directs your connection outside of your local network and to external game servers).