The first thing I did was preview it, put in my email address, and click the button. In preview mode, which rich client mode, it pops up a window asking if I want to send an email to the specified recipient with the specified subject using Outlook, which is my default mail client. I click yes, and the email showed up right away with the sender being my Outlook default account. The form was embedded in the email as expected and had the proper info.
I then published it to my SharePoint site, opened it in the browser, and again put in my personal email address. No prompt this time, and the email showed up right away, but this time the sender was the email address specified in the Outgoing email settings of Central Admin. In order to properly publish it as a browser form, I published it to a doc lib instead of administrative approval, which required setting it back to Domain trust, which could only be done by de-selecting the checkbox for making it viewable by mobile devices. Did you have that checked on purpose?
Anyway, both scenarios worked.