I got what they meant by "OS" about 10 seconds after landing on the page, but I still think it's a bad term here. The system is not controlling the operation of the home or of the people within it. It's a home-centric to do and calendaring app.
I think the disagreement comes from the interpretation of "home" or "household". You might assume a HomeOS would operate all of your smart devices in your house or something like that, which would be fair. But if you think of the members of a household as being an essential part of it (which they are) then a HomeOS is also a fair description of something which operates on those members' behaviour.