Amazon/AWS is not going to fail because Target took away their business. But Target could easily screw up transitioning to another provider, and end up paying a lot in terms of money and wasted effort. Money and effort that would have been better spent improving their core business. Target should concentrate on build a better retail business than Amazon, not worrying about whether that business is built on top of AWS or some other cloud provider.
It's like how Apple compete with Samsung in the smartphone market, but still relies on Samsung as a central component supplier for many of their devices. I'm sure Apple execs would prefer not to give Samsung any money, but they're also smart enough to realise that using only non-Samsung suppliers simply for the sake of it would ultimately be a self-defeating move.
Which is why AWS would never do this in the first place.
https://www.geekwire.com/2011/target-finally-parts-ways-amaz...