I think this is a new theremin. I certainly haven't seen one like it before.
So what can we tell from the description and audio and video clips?
Well, it's a brilliant concept (I know this because I had the same thought a few months ago :-) a pitch only theremin with optional volume only theremin. (This means you can intercept the pitch only audio before it gets to the volume theremin - interesting for performers who use pitch preview - an audio feed to an earphone, so that the player can hear what note they will play when they raise their volume hand - amongst other things.)
If it's claim of six octaves over 70 cm is accurate then that is a reasonably playing field.
It is hard to tell how the instrument would sound near the hands of a skilled player - not least because playing style has some effect on timbre - but the midrange sounds quite good to me, and the low notes are ok, not so keen on the high notes - rather lacking in tone, but tunes seldom call for them anyway.
As to the linearity I will leave that assessment based on the video (which even has a ruler set out to allow you to see the linearity better - there's confidence for you) to someone with a better ear than me. I suspect it is comparable to an etherwave. (Apparently you need great big coils to get better than that - don't ask me, I'm not an electrician - and the box isn't big enough to house them.)
Interestingly the text claims it does not operate on the heterodyne principle, and does have good linearity, and produces a very pure sine wave. Doesn't sound like it to me. But then I am relying on auto-translation as I don't speak German.
Electromungo? Care to translate?