It is true that these delivery drivers will likely be able to find other employment. It's not like it was back in some of the old mill or mining towns where a single employer could make or break a community. Although it's much better than it was 100-150 years ago, and I certainly agree it's far better than slavery. So, we've made some progress since the bad old days of yesteryear, but there are many who are justifiably worried that we could be taking steps backward, which could be a problem.
I would also add a slight caveat in regards to news stories like this, since a lot of conservative economists and business leaders have been arguing and fighting tooth and nail against minimum wage increases. So, it's like they're trying to "send a message" with a veiled warning that more jobs could be lost if there's continued pressure to raise the minimum wage.
But even then, there's a trade-off. A major complaint one hears across the board from customers is the overall decline in service from the various restaurants and retail establishments they frequent. Businesses may wish to cut to the bone and pay the lowest amount possible to their employees, but then that leads to high turnover, which can compromise service, among other things. It may not be just the pay either, as there might be other factors and working conditions which can be discerned by the customer in terms of poor service. Or, as companies like Starbucks found out the hard way, a poorly-trained and/or incompetent employee can screw up so badly as to cause a major lawsuit against the company. You get what you pay for.