I could find zero information about the input lag for the new version of the 4k Xiaomi projector so I decided to give the information out myself.
I have played both Forza Horizon and Rocket League and IT WORKS to play them. I don't know what the input lag is but it is low enough to play the games. You probably don't want to use it to play Rocket League professionally but it is certainly playable for casual players like me.
I recorded and uploaded a video on streamable playing forza horizon. You can't see the projector in the video but it's not fake. Maybe later I will create a better video.
https://streamable.com/ur2dbh