Java EE7 consists of a bunch of \"bean\" definitions:
The javadoc of Transactional says:
The javax.transaction.Transactional annotation provides the application the ability to declaratively control transaction boundaries on CDI managed beans, as well as classes defined as managed beans by the Java EE specification, at both the class and method level where method level annotations override those at the class level.
So, your assumptions are wrong. EJBs, until Java EE 6, were the only kinds of components to support declarative transactions. The Transactional annotation has precisely been introduced in Java EE 7 to make non-EJB, managed CDI beans transactional.