Thanks, Marcus. On that CCM paper, I think their approach is great and I'm happy that a whole community of researchers have been working in that direction. With this paper in particular though, it's mightily complex, and I worry that with each step of complexity they're getting further away from good physics. This is often the case with research programs that get popular -- there's a tendency to pile on complications, constructing more and more theory until it becomes a bit of a nightmare. And though I do think this is happening here, at least it hasn't yet gotten as bad as strings.
On the content side, I think I see some of what they're doing, and it is getting closer to my work. Their [itex]M_2(\mathbb{H}) \times M_4(\mathbb{C})[/itex] algebra contains the [itex]su(2) \times su(2) \times su(4)[/itex] Pati-Salam model, and they're presumably getting gravitational degrees of freedom from the rest of [itex]M_2(\mathbb{H})[/itex], though I couldn't see quite how in their paper. If that is what they're doing, then they could embed that algebra in [itex]spin(4,4) \times spin(8)[/itex], add their spinor representation and triality, and be looking squarely at [itex]E_8[/itex].
I do consider them my closest competition. But I'm not especially worried, because my approach is to minimize rather than expand complexity, which is a terrible strategy for building a career but possibly the best for figuring something out.