A videogames source code tends to be split into 2 main halves, game engine, and game logic. The game logic would be the main loop, media loading, variables, menu system etc, and would use the game engine components to handle the graphics, sound etc.
We could say that DBPro has the main components of your engine built in, then you'd probably have custom functions for the parts that aren't covered, either coded directly in DBPro or added as a plugin.
There is always some overlap between the engine and game logic, because you might not be able to just take a game engine, and write a different game - for example GTA4 and Red Dead Redemption both use the same graphics and sound engine, but the engine will have custom functions specific to whatever game. A lot of the game logic, if not all of it would be scripted code, probably precompiled into bytecode that can be interpreted quickly, and this will mostly use customised functions in the engine.
Personally, I think the confusion arises when people talk about single function engines, like Direct3D, or OpenGL - these are graphics engines, and would obviously be part of the game engine. These systems really need a game engine 'layer' on top of them, to provide functions for handling 3D objects, displaying graphics, that sort of thing. Really, that layer is present in all game engines, that's where DBPro really lies - between DirectX and your own code. I guess I'd say that DBPro is both. It provides a higher level language for game logic, much like an engine might use scripting, but also compiles it all into machine code.
So DBPro is really a hybrid of compiler and engine, it's a mongrel! - so your both right
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