Taken literally, that proto-holodeck would be HUGE. Similar size to TMP's Recreation Deck, perhaps?
I've been thinking about that. Could be the holodeck was already 'on' and in a standby screensaver mode (said mode being an infinitely large white space); otherwise you'd expect to see some kind of emitters or projectors on the walls. If that's the case, then the proto-holodeck's no bigger than the ship's gymnasium. (Nor would it need to be, at this early stage with a ship that size.)