Cave Cohnson puts it nicely, but to add some more detail, I think a lot of that research was motivated by rocket science (the actual one).

Suppose you want to increase the vertical speed of your rocket. If you just put in bigger engines and a larger fuel tank, you wouldn't have won anything: Sure the engines will provide more force, but you also increased the mass that the force has to move.

What you actually want is a more efficient fuel that gives you more power for the (approximately) same mass - you quite literally want more bang for your buck.

Because the required forces and mass constraints are so extreme, the number of possible fuels that are efficient enough for your purposes are quite limited - they are commonly known as "explosives".

As rockets with more cargo space are needed, so grows the need for even more efficient fuels - driving the development of compounds that are even more hellishly explosive than their predecessors.

Per the old Cave Johnson quote, "Science isn't about WHY. It's about WHY NOT."

As for applications - military, civil engineering, maybe even rocketry.

I have to agree with the previous commenter, but in a more serious fashion. It's not just about the fun. A lot of modern technology is possible not because someone did some directed research but because someone thought about if something could be done and how to achieve it. Sometimes it may even take generations before a small piece of knowledge suddenly finds an application, and then it can still lead to breakthroughs.

Certainly not all, but some people need to be able to do things without apparent meaning, including artists and (theoretical) scientists.

Follow the money:

"This work was supported by the Army Research Office (ARO) in the form of a Multidisciplinary University Research Initiative (MURI) (grant number: W911NF-13-1-0387)" -- from the acknowledgements of the paper.