This seems to get covered every year. Whether a team is big/mid/small market is determined by DMA's (Designated Market Areas). DMA's organize around major cities and then include surrounding areas. Everyone always wants to lump in surrounding cities to various team's DMA's, claim those populations as strengthening that team's market share, and conclude small market teams are big(er) market teams. That's not how it works.
The issue is what DMA's their cable contracts cover. Just using San Antonio, they're competing with Houston and Dallas. They obviously lose out big in the population war to those two (much smaller DMA), to say nothing of the money and influence those cities carry in the state. It's entirely possible Spurs games aren't even available in Austin. By consequence, their cable contract isn't likely to cover any great ground. Which means it makes them a LOT less money than Dallas or Houston.
San Antonio + limited coverage through Fox Sports (presumably) = lower revenue contract = small market.