The one on eBay looks to me like the face is just too soft. I see that in a lot of hammers, especially projects made in metal shop.
If there was only one, it would be an oddity an individual's quirky idea. But two of them, unrelated to each other make a pattern. I just don't know what the pattern was supposed to do, or improve. The thinned area around the eye, like on the Heller cross peins and straight peins, had a certain currency around the turn of the last century. J.G. Holstrom's Modern Blacksmithing (published 1904) insists on the pattern, and shows a picture of a common cross pein, saying that:
"No smith should ever use a hammer like [this] I have not yet been able to find out what it is good for. Too short, too clumsy, too much friction in the air. I have christened it, and if you want my name for it, call it Cain's hammer. It must surely look like the hammer used by him, if he had any."
Elsewhere, he refers to it as a club.
