In Parallels you have a few choices of how to connect to a Network or Internet, Shared Networking, Bridged Ethernet Networking and Host-Only Networking. In all of these the Guest OS/VM only sees a Wired Ethernet Adapter as that is what the software provides. It does not provide a Wi-Fi Network Adapter even though the Guest OS/VM can connect to a Network or Internet using Shared Networking or Bridged Ethernet Networking (which can be bridged to the Host's Wi-Fi or Ethernet adapters) and does not show a Wi-Fi icon in e.g. the Windows Taskbar System Notification Area. So even following the directions in Using WiFi in a Virtual Machine which uses Bridged Ethernet Networking the connection in the Guest OS/VM will still appear as a Wired Ethernet Connection.
If you want to have direct Wi-Fi connectivity in the VM, in other words have a Wi-Fi icon in e.g. the Windows Taskbar System Notification Area as if the virtual machine was a physical machine that had a built-in Wi-Fi Network Adapter, then you will need to supply your own USB Wi-Fi Adapter and connect it directly to the VM. In this scenario there is no other way!