IE advanced settings have an option "Go to an intranet site for a single word entry in the Address bar" for this exact reason
a) that's in the Advanced Settings, which is tantamount to saying "Here be Dragons" to the average user.
b) The sentence used to define that setting is also not exactly crystal-clear to most people, I would wager.
c) I completely missed it, despite trying to work out what on earth many of the settings were meant to be doing.
d) The rest of the web sites I have on my server don't seem to require this setting; they (and the Chrome Browser) seem to function very well when just given the server name.
And once again, thank you to CptJack for cutting to the chase and providing the solution.
Oh - and I've just checked that setting, restarted IE, and it has no effect on the HG web. It still does not render as it should. The only way to see the HG site on my server is to supply the IP address as CptJack suggested.