Extracting natural gas from pingos is likely not cost-effective.
From the article cited in the question:
A count of 7,000 pingos, alternative included, was likely an
underestimate, in Romanovsky’s view. Across the entire Arctic
permafrost, he estimated there may be as many as 100,000. But he could
not say how many fell into which category — a symptom, in part, of the
relatively poor resolution of imaging satellites that travel above the
tundra.
While this sounds like a lot, the "alternative pingos" are the ones which contain methane (the primary component of natural gas) in sufficient concentrations to be considered explosive. They are a tenth the size of the "traditional" pingos, measuring 50 to 100 meters across.
The article also says that only a "handful" of these alternative pingos have been found, and only as craters -- after the bubble burst.
Thus, several factors combine to indicate that extraction of natural gas from alternative pingos would not be cost-effective:
- The quantity and distribution is not well known
- The pingos must be found before they have burst
- Each pingo is small, and only yields one harvest
- They are located in remote regions with limited infrastructure
Shale gas productivity is up, and costs are down.
Even if a path to cost-effective extraction of methane from pingos could be proposed, there is little incentive to spend money in this direction, as other sources currently exist -- namely, shale gas plays in North America.
Production from shale gas is increasing rapidly:

...while at the same time, costs over the last several years are declining:

A possible "next" source of natural gas -- methane clathrates -- is already being explored.
From the BBC:
China has for the first time extracted gas from an ice-like substance
under the South China Sea considered key to future global energy
supply.
Methane clathrates (also called methane hydrates) are frozen deposits of natural gas mixed with water which are located throughout the oceans, typically at or near continental shelves. It is estimated that natural gas stored in these deposits is equivalent to ten times the quantity in on-shore shale gas deposits.