'Go out' could mean one of the things you say, and a native speaker wouldn't use it in the situation you describe. We would say, "Get out!." [Leave the room!]

You could say 'go and play somewhere else'.

Not knowing how much he understands English, I would start polite and detailed like this: "Please leave this room now, so I can work in peace." If that seems too complicated for him to understand, or he is simply not respecting your request, then make a shorter more assertive instruction next, like this: "Please leave this room!" "Leave now!" If he seems to not understand clearly, I would now resort to very fragmented instructions, with over-simplified grammar, to help him understand. For example: "Go out!" "Outside! Please!" "Not in this room!" "You go away!" "Leave me here alone!" "You go outside! I stay here! I work! You go!" Hand gestures can be very helpful at this point. Push him out the door if needs be! Good luck.

Can you please leave the room? I need it quiet so I can work. Leave the room now! (If the reason is already clear and the more polite phrasing didn’t work) Get out! is something that you scream or say in an emergency or in anger.