This vivid simile is an interesting one to try to unpack. Owen describes the "hanging" face of a soldier who has been thrown into a wagon. His eyes are "writhing" in his face and his lungs are "gargling." He is evidently a horrific sight, and when Owen describes his face as being "like a devil's" it is easy to understand why. The man no longer looks quite human, but as if he has been transformed by the "sin" of war into something less than human, like a devil. Possibly, Owen is alluding to the paintings of devils often found in English churches at that time, in which sinners in hell become devilish and are depicted screaming in agony as they are tormented.
If a devil is "sick of sin," the implication is that the level of sin must be truly deplorable. A devil is supposed to enjoy sin, and to cultivate it in other people. For this man to be compared to a devil who has suffered so much sin that even he has had too much of it, it is clear that the level of sin and suffering must have been very great indeed. Owen is underscoring the sinful nature of this war and the way in which it transforms soldiers into creatures like this man, physically "corrupted" by the sins of war.