As suspected, the normals are inversed. In Blender, this is easily fixable by going into Edit Mode, selecting everything and then doing Mesh -> Normals -> Flip Normals.
Also, you have too many frames in the model when the model is obviously a static object with no animation. I would delete all the keyframes and set the end frame to 1. This reduces the file size significantly.
Which Blender exporter are you using?
My MD3 exporter exports normals perfectly, even correctly taking into account any custom smoothing groups you've defined on the mesh.
Speaking of smoothing groups, this is more of a subjective and artistic opinion, but personally I'd shade the a barrel this way:
Add an edge split modifier and mark the edges sharp as I've illustrated. My MD3 exporter script fully respects this and it will be shaded that way 1:1 in GZDoom.