I don't know much about Home Assistant, but that certainly should be possible to set up. The KaldiAG API is pretty low level, but basically: you define a set of rules, and send in audio data, along with a bit mask of which rules are active at the beginning of each utterance, and receive back the recognized rule and text. The easy solution is probably to go through Dragonfly, which makes it easy to define the rules, contexts, and actions. It might be a little hacky to do, but you should be able to wire it up with Home Assistant somehow.

Although I mainly use it for computer control as demonstrated in the video, I do have many commands akin to home automation, like adjusting the lights, HVAC, etc.