There was something very similar in the local news a few years ago:
https://news.uns.purdue.edu/x/2009a/090121HeisterGelled.htmlThe claim then was that thixotropic fuels would be safer because they wouldn't leak for some reason. Except that pumping them requires applying pressure that could make them leak, and they'd then form persistent, flammable, corrosive blobs filling up equipment spaces or coating the pad instead of draining away or evaporating. Never mind the toxicity issues of whatever you'd use for gelled hypergolic fuel and oxidizer...
Now, the big advantage is that it's...denser than liquid hydrogen?
So is everything else. Why are they pretending liquid hydrogen is the only liquid fuel around? RP-1 is far denser than LH2. They also equate power with thrust and imply that's all that matters, when solid rockets are actually notably poor in performance compared to liquids, and adding gelling agents is likely to similarly reduce the performance of liquid fuels, particularly the oxidizer.
So, they've got a liquid fuel that's somewhat denser than common liquid fuels and might provide somewhat higher thrust at a cost in specific impulse, making it a good replacement for solid boosters (with the advantage of being able to cleanly shut down, before the vehicle leaves the pad if necessary) but a poor choice for the core. And while hyping the density and "power", they overlook some real advantages. For example, the semisolid nature would make it useful for things like orbit circularization: liquids slosh around and blob up in freefall in ways that can be hard to manage, and there'd be an advantage in flexibility over solids for this purpose, as you can easily adjust the propellant load to the payload.
