Engagement announcements really are not sent out any more. In fact, I can't even remember when they were. If the engagement is announced, it is mentioned in the local paper.
Often the save the date cards announce the engagement do to the fact that you are asking your guests to save the date you wish to marry and are only sent to those invited to the wedding.
If an engagement announcement were to be sent, it should only be sent to those invited to the wedding. But, these may be viewed as a plea for an engagement gift.