yay for all people with multiple accounts getting tons of alpha invites when some of us just want to play it on our main account and not be greedy so that the rest world can play the alpha. I got that same email and got a response back from them:
Thank you for contacting the Square Enix Support Centre.
The e-mail is not to be considered as an acceptance of any sort, we apologise for any confusion.
However it seems that a few more player were invited to apply for the Alpha testing. We would therefore recommend that you fill and send this application, regardless of your previous application.
We hope this helps and that you will be shortlisted for the testing.
Kind regards,
The Square Enix Support Centre team
Thank you again for contacting us and for your interest in Square Enix products!
More help and information is available at the Square Enix Support Centre website.
http://support.eu.square-enix.com/