So, I was told that online multiplayer games are pretty much an impossibility in Scratch now that there have been such limitations placed upon the cloud variables. But as you can see, for a turn-based game at least, there is still a lot that you can do. Click on a cat/chess piece then click on a square. I used 2 different browsers at the same time to test this, but I believe it should work for any computer anywhere.
While this may seem simple (and it is really) This can be built upon in creative ways to do things such as make a multi-player chess game or a board game or a turn-based adventure rpg game. You can have as many players as you want, just add more pieces and change the number accordingly. Anyone can control any piece. But you could create some conditions to ensure it is a certain user before certain pieces can be moved. I may do that exact thing later. The same sort of trick can be done for AI enemies and still be under the Scratch limit but they too would have to take turns. With a little extra thought, I still believe that even a fairly complex multiplayer game can still be made (at least in the turn-based spectrum). Now when it comes to action games where all the players have to move at the same time, it is probably still possible, but it will be much more difficult to achieve. I do not believe that things which use ridiculous amounts of data such as machine learning for example should ever be used on the Scratch site because it just was not designed to handle such a load of information. Storage and bandwidth do cost money and I find it a bit irresponsible of people to use it for such unwieldy things. It should be used as it was intended, to help people learn how to code and better develop their thinking processes and maybe even social skills to some degree. There is no reason to expect to build the next massively multi-player fast paced action with zero lag ultimate game of all time within the confines of Scratch. If you are at the point where you are really that advanced, you should definitely be using a better tool for the job anyway. There are plenty of game design engines that would do a much better job and run such games much faster than Scratch can.