I think you should see vert.x more as a platform. On this platform you could build a technology aimed at competing with or replacing JEE app servers. Equally you might build just those elements of a stack you need for your particular use-case.
For example, the yoke module turns it into a convenient dynamic content web server, into which you can embed business logic, and connectivity to other systems, so you could if you wanted replace a JEE app server with it. Whether it's worthwhile doing so kind of depends on your own use case, scalability requirements etc. However, that is just one use for vert.x. You could use it as essentially an actor infrastructure within another application, for example.
As Mark says, it's at a lower level than the app server. Like all platforms, it's what you choose to make of it.