Ok, maybe we need a further step.
The BIOS only recognizes a keyboard device and only if connected through the "old" DIN bus or more recently the PS/2 one, whilst most implementation (which as a matter of fact often fail/cause issues) on more recent BIOSes add an additional layer (which is sometimes referred in BIOS as "USB legacy support") that is more like a "converting the USB keyboard to a PS/2" than anything else.
Each and every "wireless" (no matter if radio, infrared, bluetooth or whatever technology) keyboard is (or should be) for all the BIOS knows a "normal", wired keyboard.
If you prefer, any device that is called keyboard presents itself to the BIOS as a keyboard, in the case of wireless keyboards such as the ones you posted a link to, it is the key that is inserted in the USB port that declares itself as "keyboard" (this is what the BIOS is looking for and the only thing that matters to it), and how exactly the USB key communicates (and couples, etc.) with the actual remote things with keys is essentially out of the interest of BIOS.
To all effects for the BIOS those "internet remote/keyboards" are just like plain, conventional USB keyboards.