Hardly unusual, there have been many developments of alternative formulations of automotive fuel, especially during the World Wars. A major reason to develop such is, of course, the likelihood of shortages in crude oil supply, refining capacity, or the desirability to use one grade of oil distillates instead of (or in addition to) another, to increase the effective output capacity of refineries.

In this case "Liberty Fuel" appears to be kerosene (which normally wouldn't ignite in a gasoline engine) along with several additives including picric acid, an explosive and chemical sibling of TNT. One major problem of using kerosene in a gasoline engine is compression and ignition temperatures, but if you spike the kerosene with an explosive that can kick start the flame front in the engine cylinder. The advantage would be being able to use kerosene grades of petroleum products instead of gasoline. Potentially, if this worked you could also use a formulation based on "bio-diesel", but I doubt that was a concern at the time.

The reason why this sort of thing was pursued then is because oil refineries were predominantly just fractional distillation systems. They separated out the crude oil into different "grades" of petroleum products and then those were used directly as fuels (or lubricants or feedstocks). This meant that the amount of whatever grade of petroleum produced was tied to its natural abundance, with gasoline being in shorter supply compared to demand than kerosene/diesel. It also meant that the overall characteristics of the petroleum products were perhaps not perfectly desirable from an industrial use standpoint, which is one reason why they began to add tetraethyl-lead to gasoline in the 1920s (which served as an artificial octane booster, decreasing pre-ignition/knocking and enabling higher compression ratios).

You can use a huge variety of fuels in gasoline engines "without modification" and immediate damage, however that doesn't exactly imply that they are just as good. Often those alternate fuels (high grade ethanol being one) will run just fine and be generally reliable but still result in an overall lower engine life over tens of thousands of miles. And that usually makes them a poor tradeoff unless actual gasoline isn't available.

Countries that faced a much higher likelihood of being deprived of access to petroleum products (such as Germany and Japan during WWII especially) pursued all sorts of alternate fuels, some requiring specialized engines. Many of these methods rely on coal (which is comparatively ubiquitous worldwide) to produce hydrocarbons.

In any event, given that Weisgerber's fuel relied on picric acid it's a fair bet to say that it might have been problematic to manufacture (due to the necessity of mass-manufacturing a high explosive as an additive component) and was almost certainly not particularly stable. It's possible that it might even be shock sensitive, which is not a desirable characteristic in a substance that people will be sitting on top of gallons of day in, day out. Additionally, after each of the wars gasoline availability, especially in the US, was hardly a problem.

Even more importantly, modern refineries use cracking/reforming of crude oil after fractional distillation to basically tune the amount of each grade of product they want. If they want more gasoline and less kerosene/diesel then they just "turn a dial" and that happens. Modern refineries transform nearly half of the crude oil they receive into gasoline, largely dictated by demand, compared to perhaps as little as 20% gasoline from natural crude (depending on grade). Technologies which were developed substantially during WWII.

Also, fuels are fairly simple industrial products. The output from the refineries is pretty much what goes directly into engines, though often very small amounts of "detergent" chemicals which help prevent soot/residue buildup in engine components are added to increase engine life. In comparison even simple alternative fuel formulations require comparatively large amounts of very expensive to manufacture additives in order to get the properties just right. Given the cheapness of gasoline and other petroleum fuels right after WWII (which saw gas prices fall consistently until the onset of the OPEC boycott) there was very little demand for alternate fuels, they simply couldn't compete on price or availability. A similar, though less pronounced, phenomenon occurred after WWI ended.

Incidentally, it appears as though the NY Times has a typo in Weisgerber's middle initial, it should be Edwin C. Weisgerber, not G. That led me to this excerpt from google books giving a hint of a little more detail on the formulation but not much, as well as a handful of patents, but none on the purported wonder fuel.

As I mentioned above work towards being able to use kerosene in gasoline engines made sense during WWI but after the war it wouldn't have been economically worthwhile and work was probably shelved after the war in concert with the massive post-war demobilization. By WWII they had different and better ideas on solving the same problem (cracking and recombination) which they pursued and came to fruition after that war, basically erasing any lingering excuse to pursue something along the lines of "Liberty Fuel". It was development of those technologies which helped drive the massive increase in automobile use post-war, because it made abundant production of low cost gasoline possible.

P.S. Also post-WWII there were significant advances in several other areas such as the development of efficient compact diesel engines and jet aircraft (and orbital rocketry I suppose). All of which made use of diesel/kerosene grades of petroleum and increased demand for those fuels. Today nearly a third of the petroleum products squeezed from crude oil are jet fuel and diesel fuel, significantly more than the roughly 10% abundance in natural crude oil.

P.P.S. I dug up a possibly related patent: US1271114 "Organic compounds containing nitrogen containing at least one nitrogen-to-oxygen bond" (though not by Weisgerber)