From their FAQ:
What are "Alternate Inbox Names" ? There are 2 ways to get email into any given inbox. When you check an inbox, listed at the top is the Alternate Inbox name. Emailing that alternate name is the same as emailing the regular name of the inbox. For example, the alternate name for "joe" is "M8R-yrtvm01" (all alternate names start with "M8R-").
So basically if you cracked the Alternate Inbox Names, you will have access to the URL of the original word used, in this case M8R-yrtvm01 will lead to joe.mailinator.com
Do you think it's possible or easy to crack? I think for that you should brute force attack their site, which will be sooner down due to heavy loads.