They showed how it developed a memory, but with serious practical limitations:
"Eventually, the same mechanic that allows the gel to retain memory causes the polymer structure to beak down to a point where it inhibits conductivity and performance reduces."
More importantly, you need a lot more than a simple and direct
A -> B logic, which I believe is all they showed. To build complex systems, you at least these elements that I think they haven't demonstrated:
- inversion
- isolation
- negative reinforcement
Neural networks derive much of their power from their layered nature and conditional pair-wise independence. Perhaps they could introduce multiple layers of gel and insulators, to achieve some degree of isolation, but you have to introduce inversion and a mechanism for negative reinforcement, if you ever hope to implement neural network-like capabilities in this medium.
So, it could indeed be a useful way to build very simple memory into objects that can't easily accommodate traditional electronics, but I think using the term "brain" is seriously over-hyping the potential of this technology. Indeed, the original paper never uses the term "brain", in reference to their hydrogel: