How do I set Zoom Player to open the video at 200%?

First press Alt-3 to set it to 200% (same as media player).

Then in "Advanced Options / Interface", check "Auto-Size User Interface to fit Source Video resolution". Once set, any new video you open will be opened at 200% Zoom factor. You can also press the "`" key to reset the window to 200% if it was resized.