It works, but not on the principle that you're talking about. What audiophiles call 'balanced' cables (at least, when used in this application) are actually for differential purposes.
Normally, when you use a cable, there's a +ve and a -ve. The -ve is actually a ground (i.e. 0V) , and in the case of 'unbalanced' cables it's shared between L and R. Balanced cable just means that the +ve and -ve connector have the same impedance profile, or in other words, it's balanced.
In differential cables, if you connect it to a differential amp, the +ve remains the same, but the -ve is not 0V: it is actually the +ve inverted 180* out of phase. Why would you do that? For portable sources, the maximum voltage is often limited as there's a battery source: however, no-one said anything about inverting it. So, in the end, you get double the voltage. Of course, that means that you also double the noise of your source (but decreasing 'ambient' environmental noise) and output impedance as you are doubling that up from the source.
The 2.5mm cable still balanced: however, it lacks the extra connector which is used for grounding purposes. The 4.4mm has the 5th conductor to act as a ground. However, for headphones this doesn't matter as it's a passive device.
So, no, it's not snake oil as you have declared. This is indeed a cable suitable for balanced, differential purposes. However, the benefits are admittedly up to you. Usually, balanced audio just duplicates the single-ended output to produce the -ve; however, some amp/DAP manufactures are rather sneaky in that the balanced circuit is completely different from the single-ended circuitry. Sony's ZX300 is like that in that the output impedance of both the SE and BAL out is the same.