As alluded to by Eric Shain, this is more a matter of the mathematics of aging than anything about the distilling process.
The key trick going on here is that years of aging have been standardized with respect to interactions with the barrel they are aging in. While time is certainly important when it comes to aging whiskey, much more important is contact with the barrel. As shown here, conversions are done based on the internal surface area to volume ratio of the containers used to age the whiskey. A greater surface-area-to-volume ratio means more rapid interaction between the whiskey and the barrel and therefore faster acquisition of the flavors desired from aging (though the different parameters will almost certainly yield at least subtly different results).
It is important to note, however, that this is a trade-off. Yes, you can age whiskey faster using smaller/higher-ratio barrels but you'd need many more to make the same amount of whiskey. So for a smaller producer who wants to match their demand as best they can, using small barrels can be a good way to sell longer aged whiskey more quickly and in more manageable quantities. On the other hand, for a larger producer who expects to have a large demand down the road, full-size barrels are likely a better option.
So ultimately, this is more a matter of the fact that "years" of aging has an implicit "in standard size barrels" as a part of it, we just don't generally think of it that way.