This isn't just Adobe Reader. This is normal for most OS X apps that have more than a single window. It's especially especially true for document-centered apps. Word, Pages, Excel, Numbers, TextEdit, and Adobe InDesign (among others) all work that way - you can have multiple document windows open on the desktop, and closing any one document will not close the app, even if it's the last document left open.
I could dig into Apple's OS X Human Interface Guidelines to cite Apple's logic for this, but it's late.
I can understand how you'd like to keep the icons in your Dock to a minimum, I happen to go in the other direction - I've made many apps "Keep in Dock" - I happen to like all my frequently-used apps a Dock-click away.
From my perspective (I work with a lot of documents), this is like having a notepad on my desktop. I may clear the desk of all current documents, but I keep the notepad on the desk, ready for the next new note.
Now, all that said, there probably is a way to modify this behavior, perhaps with Applescript. I leave that to those adept in such things.
