I've started reading into the material on Wikipedia, but I still feel like I don't really understand how a scene graph works and how it can provide benefits for a game.
What is a scene graph? A Scene graph contains all of the geometry of a particular scene. They are useful for representing translations, rotations and scales (along with other affine transformations) of objects relative to each other.
For instance, consider a tank (the type with tracks and a gun). Your scene may have multiple tanks, but each one be oriented and positioned differently, with each having its turret rotated to different azimuth and with a different gun elevation. Rather than figuring out exactly how the gun should be positioned for each tank, you can accumulate affine transformations as you traverse your scene graph to properly position it. It makes computation of such things much easier.
2D Scene Graphs: Use of a scene graph for 2D may be useful if your content is sufficiently complex and if your objects have a number of sub components not rigidly fixed to the larger body. Otherwise, as others have mentioned, it's probably overkill. The complexity of affine transformations in 2D is quite a bit less than in the 3D case.
Linear Entity Manager: I'm not clear on exactly what you mean by a linear entity manager, but if you are refering to just keeping track of where things are positioned in your scene, then scene graphs can make things easier if there is a high degree of spatial dependence between the various objects or sub-objects in your scene.