Turing Robotic Industries is a company that has created no products to date. One article says it is mostly funded by Lugee Li, CEO of DongGuan Eontec Co., Ltd. That company seems to be primarily involved in die cast metal.
So far, none of this is important enough to be news to me.
What is this mysterious Liquid Metal, that I can't tell if it is a trademark or brand name or what?
Well, it seems to be an amorphous metal alloy with a non crystalline structure. This grants it some physical properties, different strengths and weaknesses, than a chemically similar crystalline metal. However, I doubt this is going to save your screen if you do drop your phone.
Anyways, a couple of paragraphs from wikipedia:
"An amorphous metal (also known metallic glass or glassy metal) is a solid metallic material, usually an alloy, with a disordered atomic-scale structure. Most metals are crystalline in their solid state, which means they have a highly ordered arrangement of atoms. Amorphous metals are non-crystalline, and have a glass-like structure. But unlike common glasses, such as window glass, which are typically electrical insulators, amorphous metals have good electrical conductivity."
"Amorphous metals have higher tensile yield strengths and higher elastic strain limits than polycrystalline metal alloys, but their ductilities and fatigue strengths are lower. Amorphous alloys have a variety of potentially useful properties. In particular, they tend to be stronger than crystalline alloys of similar chemical composition, and they can sustain larger reversible ("elastic") deformations than crystalline alloys. Amorphous metals derive their strength directly from their non-crystalline structure, which does not have any of the defects (such as dislocations) that limit the strength of crystalline alloys. One modern amorphous metal, known as Vitreloy, has a tensile strength that is almost twice that of high-grade titanium. However, metallic glasses at room temperature are not ductile and tend to fail suddenly when loaded in tension, which limits the material applicability in reliability-critical applications, as the impending failure is not evident. Therefore, there is considerable interest in producing metal matrix composite materials consisting of a metallic glass matrix containing dendritic particles or fibers of a ductile crystalline metal."