The Wi-Fi chipset in the computer is not used at all here. The dongle presents itself to the computer as a USB human input device, just like any other USB keyboard or mouse.
This is why you can use a keyboard like this to access the BIOS settings at boot time on a PC, which you can't do with a Bluetooth keyboard.
That said, the wireless connection between the dongle and the keyboard is subject to interference by other 2.4GHz devices.
So one thing to make sure of is to connect to a 5GHz Wi-Fi network, not 2.4GHz. And as you mentioned, Bluetooth can also interfere.
I had an interesting case of this some time ago. I was using a ThinkPad TrackPoint Wireless Keyboard II with a desktop computer on the floor several feet away. This keyboard can either use Bluetooth or its own USB dongle; I used the latter so I could access BIOS settings.
It worked great - except when I used my Bluetooth Apple AirPods with a phone (either iPhone or Android). Then the keyboard would start missing characters or repeating them wildly.
The solution was to use a USB extension cable to put the keyboard dongle on my desk near the keyboard itself. That improved the signal between the two and eliminated the Bluetooth interference.