I read through the comments on the Thingiverse item, and sort of laughed when the originator said supports shouldn't be required.

You have to think about how these FDM printers work - a new layer is "squished" onto the layer underneath it. When you get into an overhang, well, there's less and less to squish onto. Simple as that. This is EXACTLY what is happening in your grey print without supports. Up to a 45 degree slope should be easy peasy, but this model requires far more severe of an angle than that. Have you tested your printer and slicer settings on a calibration model that tells you what your setup can do as far as overhangs?

I don't know what kind of pixie dust the Thingiverse originator has to use with his machine, but if I dared to attempt the model it'd have to be with a lot of supports, a just barely hot enough temp and some pretty extensive cooling airflow, hoping to freeze the filament before it had a chance to droop, whether that droop was onto almost free air or onto the support structure.