No, they don't pay a fee.

You pay a fee for making a purchase. Local retailers should be arguing that they don't want to be the tax collectors, so their prices would look lower too.

Either way, you, the buyer, are responsible for paying the sales and use tax, regardless of whether you bought from BestBuy or Amazon.

Again, both BestBuy and Amazon "get to do business without paying that fee", as it's not something either of them pays.

To enjoy the competitive advantage of having a local presence, BestBuy does agree to help your local government collect your taxes (and in fact gets to KEEP a percentage of the taxes they collect!), while Amazon, who is not in your local jurisdiction, relies on you to pay the tax you owe.