Nothing in this paper is actually new. Its a review. In general understanding various uncertainty principles is pretty foundational in engineering quantum things, for example transistors. They're also an essential part of how we understand electromagnetic waves from radio through WiFi and xrays.

In terms of direct engineering implications I think there are essentially none, but this is in the background of a lot of important stuff.

The way I interpreted it they're claiming their mathematical approach to relating the wave uncertainty in FFTs to uncertainty formula in Quantum Mechanics is a novel one. I don't think there's any actual new discoveries however, because there's an infinite number of ways to show that all of mathematics is internally consistent. However I have great respect for all their math, if it's all correct, and it may be useful to someone just like when Einstein "found" Lorentz formulas and Minkowski space which were done before him and ready for him to recognize the pattern that fit into his own tinkerings that we now call relativity.