A company which is selling goods over the Internet and has a presence in the state of delivery, ie has established a nexus in that state, will be required to collect sales tax on all taxable goods. NY argued that Amazon had the nexus, Amazon lost and so charges sales tax.
Without the nexus, the Supreme Court has prevented states from imposing sales tax on out-of-state sales.
However, in those cases, the individual is required to fill out the use tax form when filing taxes. This is difficult to enforce, and so largely gets unpaid.
So everyone is supposed to pay sales tax.
As for shipping costs, as said, it may be less than $3, it may be much more than $3. But large businesses don't necessarily attach shipping costs to every item sold, factoring the profit/loss in such a small manner.
Instead, shipping costs are usually aggregated, and the losses from that unit can be justified if they generate more sales, much like promotions or marketing. As long as the profit margin on the unit sale is large enough, the increased sales from free shipping is usually a good thing.
With gamestop especially, when you can explicitly see their markup (just subtract the cost of buying a used game from the the trade-in price), you can see in that healthy area they can very much afford a few dollars lost to free shipping.