The article is garbage because the author didn't provide any actual insight into whether Southwest is gaining market share in the current environment or not. Unfortunately the DOT statistics are only up to date to February, but it would have been easy to pull the 10Q reports for all the major airlines for this year and last and compare passenger totals. Or pay a little money for statistics from one of the companies that provides industry analysis.
The article is correct though that it isn't clear that having a larger market share now will result in a larger market share once we are past COVID. Different airlines are taking different strategies in dealing with the pandemic and it is too early to say who will be proven right. For example, United and Delta were far more aggressive in Q2 on holding the line on fares, and chose to not deeply discount in order to chase the few people that were traveling and the minimal revenue in the market. Both actually saw yields increase year over year. They want to preserve pricing power post-pandemic and not spend years rebuilding toward profitable fares. American and Southwest flew far more capacity and slashed prices to grab more of the few people traveling, hoping to steal frequent flyers away from competitors while snagging as much revenue as possible now.
Also, when airline analysts like Hunter Keay discuss capacity they are usually using a statistic called ASMs, Available Seat Miles, and not number of flights. Right now it is a messy statistic because some airlines have decided to reduce capacity on flights to ensure middle seats can remain open but those middle seats still count as ASMs, while others are booking to 100% capacity.