Do you use the Amazon Echo provided by your hotel in your room?
The hack described here requires the attacker have physical access to the target Echo. So the one in your house might not be so much at risk (assuming you have reasonably good physical security for your house and your kids’ friends are supervised any time they are in the house). But any Echo that is accessed by many people in unrestricted physical access, are potentially compromised.
This seems like an echo (ha ha) of the Furby ban at the NSA since there was a concern that the toy could record audio and replay sensitive information. The Echo, however, can and does actively listen to your conversations, and is connected to networks so your conversations can be recorded or broadcast anywhere it is directed.