This thing seems to be mostly an interface for other home automation devices. In the demo, it doesn't directly control anything important. It's not like there are motor control relays connected to the Raspberry Pi's GPIO ports. A big question is how this fails. It needs to fail into some safe condition. Raspberry Pi machines have a full Linux and no stall timer, so they can end up crashed or hung. If this thing turns…
https://home-assistant.io/components/rpi_gpio/
Home Assistant is indeed an "aggregator" for a lot of different home automation devices. Personally, I find it very useful to have my Nest, my ZWave devices, various ESP8266 "things" (garage door controller, temp/humidity sensors, my doorbell, etc), along with my Chromecasts, and the home/away status of my wife and I all rolled into one state machine (plus a lot of "general" information... the time, sunrise/sunset timing, current weather in my area, traffic conditions, etc).
Having all that information in one place means those various components can be controlled intelligently, based on all the available information, rather than just the small island each of them would be on their own.
A Pi is totally optional, BTW. You can run HA on pretty much anything that runs Python3.