"Is that so?"

Yes.

"I am not sure why there would be a noticeable latency."

Even if you don't understand it, the latency will still affect you.

"Wireless keyboards and mouse works fine from a distance."

Yes, they do. That's irrelevant. They don't use wi-fi, and they transmit significantly less data than used in a video signal.

"Besides, I am not suggesting using wifi for this, but a direct radio link."

You are suggesting using wifi. Your comment, to which I responded, included a link to an HDMI stick which streams video over wifi.

I'm suggesting that the device you linked (along with every other HDMI/wi-fi stick) will not serve your purpose, due to latency.

Feel free to buy it and report back your results if they differ :)