The tool is here in action in one user's Instagram video. It is some sort of vacuum machine. However, my normal vacuum cleaner is not so powerful. I am not sure if there is any chemicals used in such a cleaning procedure because I have never managed to clean such a way.
I believe that this is the exact machine used in the video Daimer Carpet Cleaning
This is obviously a professional tool which would be out of range of most consumers except for professional service companies. Here is an Amazon alternative. BISSELL Portable
But to answer your original question, the first link is the one used in the video (pretty darn sure)