In Seattle, wages for low earning employees increased roughly 10% with negligible negative impact on the local economy. Everyone was able to raise prices enough to offset the cost and they weren't at a price disadvantage with local competitors were all in the same situation. Walmart also raised its own minimum wage and they didn't exactly go into a hiring freeze.
Unless your business is a small business is a service company (plumber, janitorial services, landscaping, IT outsourcing, law office, day care, etc.) then the top cost should be cost of inventory. Darden restaurants (Olive Garden) spends as much on food as labor, and Walmart's operating/selling/GA expenses are 20% of revenues and are smaller than COGS.
Small retailers like those mentioned in the article are at a major disadvantage in the marketplace.
What small business owners should expect is declining store traffic as people do more shopping on their phones. Either these small shops aren't online, or they're on marketplaces like Amazon where they're competing against hundreds of other sellers where the lowest price wins the Amazon buy box and Amazon gets its share regardless.
It doesn't matter a ton whether small businesses pay their employees $15 an hour or minimum wage--higher salaries will just speed up how quickly automation replaces worker for low value tasks. Grocery stores have offered self checkout for years, and large fast food chains are testing systems where customers place their own orders. Amazon has automated large parts of their order picking and is testing drone delivery systems that could eliminate delivery drivers in some areas. Even doctors and lawyers aren't safe--companies already offer computerized systems to replace junior associates at reduced cost and higher efficiency, and surgical robots recently outperformed human doctors for a specific procedure (robots won in every measure except speed).
Blockbuster Video was a pretty big company until Redbox and Netflix killed it. Small retailers are going to be eaten up and it won't be labor costs that do it.