Short answer: Yes, its fake.
Long answer: It is possible to send "fake" emails, or rather fake the domain the email was sent from by using your own SMTP server. An SMTP (Send Mail Transfer Protocol) server is where email originates from. Mail from Google's SMTP servers shows that its coming from the @gmail.com domain. If you go to the trouble of running your own SMTP server, you are allowed the ability to designate what domain the mail is being sent from, or in this case supposedly sent from. In reality this isn't something that's difficult to do, I think it's uncommon mainly because 1) the sender isn't able to receive a reply to whatever they send since they aren't using an email address they actually have access to, 2) some mail servers/clients detect that the sender is fake and alert you of such (Gmail is one I have seen do this), 3) many people just assume that email is secure and it's not possible to edit the sender name or domain, 4) it is illegal in many places.
I share this because when I realized how easy it was to fake the sender address I was surprised. I was interning at a software company creating workflows for inter-office communication and when prompted with entering a value into the "from" field I realized you can actually use any value.