Cube 2 requires individual meshes to be indicated by OBJ groups, not OBJ objects, which is probably not default behavior for SketchUp.
Nieb's simple tree-sprite model demonstrates proper form for getting your model displayed.
I don't know about SketchUp, but Blender OBJs need to be modified slightly.
The beginning of each individual mesh is indicated by "o MESHNAME". Remember that name, then find the next "usemtl" line, and above it add "g MESHNAME". Load into Cube 2 with appropriate obj.cfg (Nieb's tree example here. All you probably need is objload, objskin, and maybe mdlscale.)