Their messaging system, and they permitted the messages. How is this Amazon's fault?
eBay is taking the ridiculous stance that it's TOS provides liability to the customer for using their service wrong. If I made a website with a TOS that said "Anyone who browses to this website and fails to click the 'get lisence' button in the footer on EACH PAGE owes me $1 Million Dollars!", I'd be laughed out of court trying to enforce it.
A C&D like this is pretty standard fare between competing businesses. If you sell widgets and WidgetCorp sells widgets, you are completely allowed to try and poach their customers, but WidgetCorp is allowed you prevent you from doing that in their store. Furthermore, if the accounts were specifically created for this purpose it's a clear violation of the TOS and there may potentially be damages there, or even possible criminal charges (thanks to the wonderful CFAA - ack).
In your example, it'd be reasonable for WidgetCorp to trespass you from the store if you're trying to compete on their property. However, I believe it would be unreasonable for Widgetcorp to try to sue for the revenue of the sales that were successfully made before they trespassed you.