" adding a new intermediary device to one of the networks and connect it to one of the LANs or WANs with a media connection "
The intermediary device includes Router, L2/L3 Switch, Firewall, Wireless Router/AP.
So, Yes, what u've done is correct. I prepared a sample topology here for clear understanding. U can add router/switch/wirelessAP and connect it with laptop/desktop/smartphone as an end device.
Hope this help..