hmmm I'm not sure I follow....
"The MD will feed video to my amp?" - Correct. The MD is just a computer like any other, really, so you can connect its video out to a TV directly, or pipe it through an amp if you wish. If through an amp, you can then also use the MD to control the amp as well, if you want. Via I/R, ethernet, serial, etc. to control volume, select inputs, and so on, to minimise the number of remote controls you need.
"Is it pretty much just a dumb terminal?" - This bit I don't follow. No, its a full computer, as above, just with no HDD, it mounts the "core's" HDD remotely and uses that for the operating system.
To clarify - although it sometimes appears as though all the "smarts" are in the core and the MDs are just "dumb terminals", that is not actually the case. From most perspectives, MDs are the same as the core. Only really house-wide functions are unique to the core, so the telephony, security, media management, etc are all _coordinated_ by the core. Thus although the commands used to start media playback (whether the source is local to the MD or remote) are coordinated and relayed through the core, the actual playback is entirely the MD. It connects to the media source (say a NAS device, a local/remote HDD, local/remote DVD drive, Internet radio station, etc) and pulls the data to itself, then decodes it as necessary and plays it out its AV interfaces, as configured.
So the core provides the central configuration database for the whole house, Internet access and firewalling for the whole house, the house "PABX", the security centre functionality and coordinates the media streams around the house that allow you to move a stream from one MD to another. But the individual tasks like playing a specific piece of media in a particular room is all MD, so they are in no sense "dumb", even if they are in a sense "slaves" to the core and bereft of HDDs (normally)!