Lets say I have 3 machines (reachable over ssh with the same pass and username)
Let's not and say we did. Unless you're running this as a toy system completely isolated from the internet, this is not how you should be accessing a server regularly. You want to read up on setting up a server's SSH securely. Simply having a strong password is not enough. If this is not a server you own (and you aren't managing its SSH), you still do not want to use a username/password combo to log in. Use an SSH key.
and I want to see periodically updated output of a simple script ('nvidia-smi') in 1 window (concatenated) from all 3 machines.
Well, once you have your SSH set up securely, you would use the ssh program on your machine. 'ssh username@host.domain "command to execute"' will output that command's stdout to your stdout. From there, it's the same thing as "How do I take the output from three commands and print them all to my screen?"