This predicting inputs thing is literally what all online games are doing right now, this is the only way online games are still at all playable even if you have something like 200ms RTT.
After this many years, you should read up on English grammar Jo. This one reads like a google translation.
Anyway, I don't trust this technology. There's a huge risk that it will remain unresponsive, but instead of the game not registering any input, it will be given the wrong input.
The stadia controller seems like a bit of a bad idea to me.
The only reason I've started using apple arcade, is because it allows me to use the XBox One BT controller I already have, meaning zero entry-cost. Before that, the value proposition of mobile controllers was always too bad.
Too pricey for the quality. Needing a separate controller for each platform. Etc. Being able to use an existing one removed an entry barrier in more ways than only price.
I wonder if the Stadia controller is at least compatible with Steam.
Basically, the system analyzes your playstyle, pre-renders your most likely inputs from that data, and then slots them in where possible. It's trying to guess your movies so it can keep up with you.