"As an engineering manager, you'll need to put company first, team second and your team members third."

I wouldn't make this into a priority list -- whether it's right or wrong, I think it's the wrong mindset. Priority lists are hard to apply in practice because it's rarely clear who might be losing from a given decision.

For one thing, putting the "company" first is a little vague and hard to internalize. Is that the CEO? The long-term success? The stock price? With a "company" first mindset, you'll probably fall into some political games.

Instead, you should start with the actual users of the product and keep that in view. This will help solve the problem where your team executes on a project perfectly and then nobody wants it, or it gets canceled for some mysterious reason. It will also lead you to what's best for the company, make the team successful, and (hopefully) lead to rewards for the team members.