The first link is an adapter that plugs into the TV/projector and can use wifi-direct or miracast/widi.
The second link is mostly generic wireless display devices that transmit the display over an RF radio frequency and require both a a sender and receiver module.
So the first link does do pretty much what you said.
You install a software, connect via wifi-direct to the receiver and then run the software.
Here is how to select different adapters:
https://www.drivethelife.com/windows-10/change-to-multiple-wifi-adapters-in-windows-10.html
Internal adapter should have higher metric by default but wont hurt to manually make internal wifi top (and use secondary for display connection).
IP address does not matter because the device you are making a wifi direct connection to will supply you an IP, if you change it, you wont get a connection.
Your surface does have miracast/widi built into it (which means you could have wifi and miracast with the internal wifi adapter), however many users have had nothing but problems with it.
Your parts list is right that you need the display adapter, and a 2nd wifi adapter for laptop.
As stated earlier though, reliability may be less than desired, just have to see. Only 2 reviews on startech's site and 4 on amazon.