The money for a cashier to make a livable wage doesn't have to come from increasing the costs of all goods. The point of the article was essentially that companies have more money than they know what do with. If they paid their employees more, not only would it be better for the employees, it would be better for the company as more money in the hands of the poor will drive up demand for goods.
I think you mean, "If other companies(but not us) pay their employees more, then as consumers they can buy our stuff". I seriously doubt that giving an extra dollar to an employee generates more than a dollar in actual revenue looking solely at the purchases made by that employee. Maybe there are other social knock-on effects, but I don't see them spending more than $x on your own products when you give them $x.
One plausible exception would be for items so expensive that they're often financed with debt: A car manufacturing company might plausibly generate more than a dollar in revenue in the short-term if its employees borrowed money to finance it.
Another plausible exception would be if you gave someone a temporary raise, and they immediately started spending more and going further into debt(think buying a bigger house, bigger car, funding a bonus vacation on a credit card, etc.). Then when you cut their wages 6 months later, it's possible that for some items you would've convinced your own employees to spend more money than you gave them on your own products.
A third exception might be for companies that completely control the employees' spending. For example, a prison or a camp full of debt slaves might be paid $3/hour, but they could only spend it on overpriced company goods. Raising it to $4/hour still wouldn't exactly generate direct revenue over the long term, but it wouldn't cost the company much at all since they'd capture 100% of the spending. Anything short of that 100% is savings, and people might be more willing to spend down their savings if they thought money was easier to get. So you could - in the short term - make money by raising wages. Doubly-so if you extend them credit(on top of whatever debt they're working off).
I can't think of a way that the "giving people more money gives them more money to give back to you" argument actually works that doesn't involve saddling them with debt. And these are merely plausible - I don't know that they're what would actually happen.
Actually, what does them being employees have to do with the argument? If that argument were valid, why wouldn't my local grocery store hand out free $20 bills to anyone who comes in, since this would spur them to buy stuff? Or if you were truly convinced that this would make the companies more money, you could easily be a millionaire by buying up a local McDonalds(with a government-backed loan), raising everyone's wages, and then when your income goes up by x% reselling the business for an x% increase on the $300,000 or so you bought the McDonald's for(and repeating this a couple times).
