Worst case for Amazon is they maintain status quo by forcing competitors cost up. Best case for Amazon is that they drive some of their competition out of business, or take some of that business because super giant Amazon is better able to absorb the increased wage cost than smaller businesses.
It is very much like their state sales tax collection strategy. Oppose it for as long as possible, accept it, then lobby for everyone else to have to do it.
There's no doubt labour is better of in the short run with double wages. I would not doubt the effects in the long-run but that's part belief. The market structure will change, less capital intensive firms will drop out. That might be brick and mortar stores (note: bricks are capital but bricks are not really productive in the sense meant above).
Remember that the velocity of money makes it a non-zero-sum game.
EDIT: Ends up that Wikipedia covers this nicely:
https://en.wikipedia.org/wiki/Minimum_wage_in_the_United_Sta...
"The interconnection of price levels, central bank policy, wage agreements, and total aggregate demand creates a situation in which conclusions drawn from macroeconomic analysis are highly influenced by the underlying assumptions of the interpreter."
Also has a nice side-bar quote from Henry Ford, who was partially known for higher wages, and which I think addresses the point I was trying to make (emphasis mine):
"The owner, the employees, and the buying public are all one and the same, and unless an industry can so manage itself as to keep wages high and prices low it destroys itself, for otherwise it limits the number of its customers. One's own employees ought to be one's own best customers."