The email address is one that many of our emails for Beta invites etc. get sent from, but any access should be visible in the launcher around the same time as receiving the email. The advice about not clicking any potentially suspicious links is generally sound.
Sometimes you might need to completely log-out (not just exit or close) the launcher and log back in again to force a “refresh” of the account info. Then if you click on the Warcraft III: Reforged icon, if you have access there will be a drop-down menu above the dimmed install button which you can select the Beta account from and install the Beta.