PCs don't *SEE* a router as part of its hardware. It is a network device that the PC connects to in exactly the same way as connecting to a network switch - there is no Router hardware installed in the PC to be shown in either Device Manager or the Network Connections folder. It is the "Local Area Connection" which is your connection to the router, other computers in your LAN and the internet.
What you do need to have installed in your PC(s) is the software for the Wireless Network Adapter(s). The software scans for "Available Wireless Networks" and should find the one with the SSID that matches your router's. You then select the option to "Connect" to that network and, once connected, your WiFi adapter should get its IP address from the router and have internet access.