Hahahahaha I found the “problem”. And I didn’t know this either. On the editor right next to the play button click on the little white arrow for extra options and click on advanced settings. This will open editor preferences. Go to the bottom, there should be the Multiplayer Options. Now uncheck use single process and this will bring out more options. On the one that says Editor Multiplayer Mode, change that to play as listen server. And that’s it. Now click on the extra play options again and choose Standalone Game. Now try it touch the cube. It should print only once per window and it should have the correct message. Note that is harder to know who’s the server when playing in this mode but the server is usually the window that loads the game first and it appears on the same place on screen everytime.
The “problem” is that, and this is new for me, when you are using a single process to run the game in the editor the engine automatically prints everything for everyone when you are on a networked game. So all the code is correct. There is no mistake.