Check M16A1_MGMC.fxsxml. You'll see that it includes the reference to a trigger file that isn't included in the base game.
You'll need to check the trigger file for references to .gr2 animations that you're missing. Note it's also possible that you're missing sound files and effects (though the latter only work with quasi-DLC mods) that are referenced in the trigger file, though I'm pretty sure that's not the case for this one, since I recognize the filename as one of danrell's.
So make sure you've grabbed edited_fx_triggers_antiair_vehicle_4gun.ftsxml and the associated .gr2s from the original mod (they'll probably be in a folder called edited_animations) and set them to VFS=True. The location in your mod doesn't matter.