They never actually mention linoleic acid, but they do discuss lipid peroxidation and some of the products thereof, such as malondialdehyde, which are produced from LA.
"While the specific mechanisms underlying asthma have yet to be identified, there is accumulating evidence that oxidative stress from altered GSH/GSSG redox status may play an important role in the modulation and severity of the disorder."
So the molecular mechanism section is quite incomplete.
As such, it's an annoying article, as it is a missed opportunity from a mechanistic perspective, many of which have been described under other contexts. It also does not discuss the similarities to atherosclerosis, which are pretty obvious when reading this paper.
But the therapeutic approaches are sound, and validate the underlying concept of omega-6 fat involvement in asthma.
"Glutathione Redox Control of Asthma: From Molecular Mechanisms to Therapeutic Opportunities"
Hat tip to Chris Masterjohn.