I want ezQuake to display the normal HUD, i.e. the one I see when I play when watching demos. Can someone help?

It should?

Unless you have another install and your registry sees this as the install that is associated with demos (windows).
I actually have a separate install just for demo viewing.

Try /mvd_autohud 0 (do not load ant hud configs on watching demos)
Remove all unnecessary "config.cfg" files (also from your $HOME dir) except one located at <q1dir>/ezquake/configs/