If you're talking about the relationship of engineering management with senior management, the most important "core skill," though I wouldn't really call it a skill, is alignment. Thing is, you won't get alignment without being closely aligned with product management, and if product management is weak, acting just as a features accountant, you're screwed no matter how good an engineering manager you are. You have no support to disagree with or shape senior management inputs. Everything else is nice and correct but not determinative the way that alignment will be.