Your file exports just fine here in DXF. Some points to check:
AI has a concept of a “canvas” of a specific size. In fact the dxf may be fine, but your objects may be off the canvas somewhere. You can try moving your objects closer to the origin before exporting and make sure the canvas in AI is big enough to accommodate them (the objects are a bit bigger than 300mm square)
Don’t export the polysurface in the DXF, AI will not necessarily understand that.
I might also try not to have the $ signs in the layer name - obviously this was on a sublayer in Rhino, the :: sublayer separators in Rhino are converted into $ for DXF export. Try moving the objects to a parent layer and re-exporting.
If all that fails, please run SystemInfo in Rhino and copy/paste the results here.