Everyone's pointing out that these can be saved and they address this in their FAQ. It seems the purpose is not to stop the other person viewing the message more than once on their end (snapchat-ish) but to stop emails being recorded by email providers/governments.

EDIT: Looking through their privacy statement:

"Hence messages are to be sent at the risk of the user. Information such as messages, time, date, name of the receiver and sender are also logged by us. We also collect and use aggregated or de-identified information."

IANAL but that looks to me that they are storing messages?