After reviewing, I could find no issues. I then looked at the image you posted and I'm thinking that there may be some communication error. When using the By Polygon option, every face belonging to the same polygon as the selected face will be deleted. That means that if one face of a polygon is selected, all faces will be deleted. The screen shot looks to be working as expected.
Could you explain to my what you intended for the By Polygon to be and how it isn't working as you'd expect? If you just want the face and not the entire polygon, just uncheck the By Polygon option. Maybe I'm misunderstanding your issue?