Okay now, that quote has the key, "nonabstract methods". Since the author means to add non-abstract methods to the already abstract class, any subclass will inherit those non-abstract methods without having to provide implementations because they are already provided (unless they wanted to override them).

Implementing an interface would require providing the code in the method body (whether or not the interface is the old or new version, but a new interface with additional methods would "break" the subclasses that used the old interface). By "break", he means that the subclasses would need to be edited and recompiled to support the new methods.