https://doc-stage.usersys.redhat.com/documentation/en-us/red_hat_jboss_enterprise_application_platform/7.1.beta/html-single/development_guide/#jboss_eap_mbean_services

A managed bean, sometimes simply referred to as an MBean, is a type of JavaBean that is created with dependency injection.

This sentence conflates two different things

• MBeans as a means of managing JVM instances using the JMX technology
• managed beans from the Java EE world, related to CDI

MBeans (the JMX ones) are actually NOT created with dependency injection, unlike the CDI managed beans.
The description should also say that MBeans are used for representing a resource which can be managed (in EAP case, it can be any resource from the standard management model).

MBean services are the core building blocks of the JBoss EAP server.

I wouldn't exactly say so, MBean services are just one way how to manage EAP instances. Writing custom MBean services is useful when one wants to extend the standard JMX management capabilities with some new functionality, which can then be managed from a JMX client.

Also, do we really need the section 8.2. Deploying JBoss MBean Services? It basically only repeats how to deploy an application to a running instance, there's nothing specific to MBean services. How-to for deploying applications belongs just under some general management documentation, here it just decreases the signal-to-noise ratio, I would say.