Reliance on a changed/wrong credit card number isn't the way to cancel subscriptions.
I doubt there is any wrong doing by amex or roku/espn, until you cancel the subscription it could be assumed that you still want it.
I've had cards with expired dates magically reused before I was able to update the expiration date. Not always but it has happened before...
If is a recurring transaction (in this case, streaming) the network will try to pass the charge, even if the original number is no longer active. In this case, even when you have a different card/account number, it still the same account. If it was a one time purchase, like buying something on eBay online, the charge would not approve since the card is not active. You can try contacting Amex to see if they can unsubscribe and block the charge, since it's recurring. Hope this help 
Many merchants with recurring billing subscribe to services that allow payment updating when a card number, expiration, and/or CID has changed. Amex has offered that for nearly 20 years on their network. The boilerplate script read over the phone (or written online or in chat) for cards across all payment networks when reporting fraud or a card that has been lost or stolen clearly states that recurring billing charges may still be allowed.
The reason these are allowed is that your card issuer can clearly see that you authorized previous charges from a merchant with a subscription service or other recurring billing, rather than a new charge from a merchant you had not previously been engaged with. In most cases, this is a convenience for both the consumer and the merchant.
I would not dispute the charge with Amex, as that would be a frivolous chargeback since you clearly authorized recurring billing and it would have been disclosed when the card was replaced. I would contact ESPN+, let them know that you have duplicate subscriptions, and it is likely (particularly if this was a recent renewal) that they will issue you a credit.
Sometimes it happens when you put a card on a recurring subscription. The bank will still allow the charge to go through because it is recognized as a recurring subscription, even if the card number changes. I see where you're coming from, though if it was true fraud, you could fairly easily call them up and tell them.
Yeah recurring charges will go through. They do that so you don't have to update your payment info when you get a new card with new expiration and CVV every few years.
Never count on your payment method going away as a way to get rid of a subscription.
