I never connect a keyboard/monitor to my pis – always run them remotely. Though I’m not using a desktop, just doing things the old fashioned way with a text terminal, so no need for remote desktops. No good if you want a desktop or aren’t comfortable with a purely text interface, but to be honest you can do most stuff people do with a pi that way. I’m using PuTTY to do an SSH connection (and mounting shared directories so I can edit files on my laptop which then appear on the pi as native files – also WinSCP is a useful tool for transferring files from a laptop).
Unless I’m missing something sharkbait, that demo is using the pi as a client, so not what jam is after – I’ve also used a pi as a Spice client to run a Windows VM from a server (though it struggles a little with performance for that).
No real advantage to HDMI over DVI – the cables are just as cheap as no conversion required, it’s just a different plug. Conversion required for VGA, but the converters are so cheap that’s not really an issue either – I’ve got one of these which works fine.
I think the idea with the pi was that most people have an HDMI TV to plug into, but even if you’re still in the dark ages like me, the composite video connection actually works OK if you’ve got an old telly to plug into.