Windows Media Player (comes with Windows 10) does that when you press ctrl+3 or View>Pplay now window from the menu. Comes close enough to your requirement to be useful, I think.
In 2006 I had a media player that use to auto pop-out a 2nd smaller float window the moment you click away.
A current example of it is a feature that is used in Skype during video chat on PC at the moment.
I forgot the name of the program I was using at that time and I am sure that some media players have this option today.
I tried downloading a few of the media players today but I could not find it.
I need help to find the software that works on Microsoft Windows that has this feature.