How could this fossil's soft tissue be preserved so well?
You're right that the authors don't comment on how they think the fossilization occurred. Since that process isn't the point of their article, my guess is that any discussion of it would have detracted from their research focus. 

There are some ways that soft tissue fossilization can occur, but to specifically answer your question as it relates to this case, you'd have to know more about the geological conditions in which the fossils were found, which I don't see in the article. This article provides a nice review of soft-tissue preservation processes. 

The main points to consider in soft-tissue fossilization, according to the linked article, are pressure, time, charge and chemistry.

Pressure: How much pressure was the fossil under? The higher the pressure, the less oxygen and fewer organisms can access it and degrade biological tissue.

Time: How quickly did the fossil become inaccessible to degrading organisms? The faster this occurs, the less likely that any soft tissue will rot away.

Charge: Does the sediment in which the fossil found carry a charge? Electrical charge acts both as an selective barrier to some organisms and chemical compounds that can hurry biological decay and provides a means for reaction with biochemical compounds, which brings us to the last point:

Chemistry: Can components of the biological soft tissue react with their surrounding minerals? If so, then the inorganic compounds present may be able to reduce lipids and other complex carbohydrates to molecular carbon and minerals in the form of the biological organism.

So say, for instance, that this organism was suddenly encased in a thick layer of clay. As the review states: 


  In clay-rich environments, the large surface area and charge of clay
  grains are thought to contribute to preservation in one of two ways.
  First, enzymes produced either through autolysis or by invading
  microbes are adsorbed to the surface of the clay grains and
  inactivated, slowing or preventing degradation (Butterfield 1990,
  Garwood et al. 1983). Second, molecules directly adsorbed to clay
  grains are resistant to degradation (Stotzky 1980), whereas
  protein-protein layers are readily degraded. This mechanism may
  explain the exquisite preservation of thin carbon films in impression
  fossils such as the feathered dinosaurs of the Jehol Biota (see
  discussion below). As tissues interact with surrounding clay grains,
  only the molecules in direct contact with clays are preserved as
  monolayers, whereas the rest are degraded normally. Thus, surface
  morphology is preserved, and original carbon might be preserved as
  well


Who knows if this process explains these particular fossils. ¯_(ツ)_/¯  As I said earlier, we'd need more information. The section quoted above, though, seems (to me) to provide a plausible hypothesis. 

I hope this helps!