So this is a winding order issue. Polygons have two sides, and they are determined by the winding order -- clockwise or anticlockwise -- of the face's vertices.

Previously, GE didn't care about polygon winding orders as both sides received the same lighting. Now, however, we use dynamic lighting, so the winding order is very important. (For reference, both we and SketchUp (and most other 3D programs) use the right-hand rule, where surface normals are declared positive with an anticlockwise winding order.) If polygons have the "wrong" order, they will not be coloured correctly.

Judging from your model, it looks like almost all of the faces have the wrong winding order, which is actually a good thing as it's trivial to fix this in SketchUp. Load up your model, select all faces (ctrl-a) right-click on one of them and select reverse faces.

Note that SketchUp also differentiates between the front and back of a face, and colours them accordingly. You should ensure that your models have a consistent winding order before exporting to GE.

(SketchUp does a great job of keeping things consistent, but problems may be encountered when importing externally authored 3ds/dwg files. Fixing the orientation of faces can be a real issue in these instances.)