Gmail – How to View Email Headers

While Lipis' answer still works, there's another method as well.

With the message open, hover your mouse pointer over the sender's name. An info card will pop up. If the address is not already in your contacts, you can click the "Add to Contacts" button to open a contact edit form with the name and email address already filled out.

(The Add and invite button is for adding the person to your Google+ Circles.)

This is a known issue with all of Google's services. They do not support the .eml or the less common .mht, both of which are known and established formats. In this case it has been (for years now) one area that all the others (Microsoft, Apple, Mozilla, and most of the rest of the community) are ahead of Google on. The only option, aside from convincing Google to support it, appears to be to either bear with the extra info and read it as a raw text file or to save it and open it with almost any other email client, such as Thunderbird or Outlook.