There are a few things that are odd about the model. It has 9,938 components in it, but only 191 of those are used. Most of the faces are using one texture, that is a texture map. It’s amazing that SketchUp can cope with that, but it seems that exporting seems to lose the UV mapping. BTW, the same symptoms do show in Unity, and Eric’s test worked there too.
What application was used to make the model, or at least to texture it?
I made a no components version. It doesn’t solve the main issue of losing the textures, but it’s 1/3rd the file size, and performs a lot better. I also tried Skimp on it, and got it down to 6MB, but it did lose the texturing at that point.
Here’s the no components 14 MB version.
Model_01nocomp.skp (13.3 MB)