How can I change x11 window size programatically?
You can install Homebrew and use it to install wmctrl using the following command:

  brew install wmctrl


Then run wmctrl like this:

wmctrl -l


It should give you a list of all the available windows on screen. Take the ID for the game window and run:

wmctrl -i -r windowid -e 0,0,0,1600,1200


where windowid should be replaced with the ID of that window.

Note: I don't think your mission is likely to succeed, as most programs that do not offer resize handles are not able to handle resizing their windows at all. You'll probably end up with the contents being the same size as always, and then just a white/black color for the rest of the enlarged window. But it is worth a try!