This is fine advice up to a certain point, but you do not accomplish bigger and grander things by working harder, nor even, as this implies, by working more diligently. You accomplish them through leverage.
It is not just about what you are working on. You need to understand what everyone else is working on, and more importantly, what they could be working on (their capabilities) and what they should be working on (the org's priorities). When you find yourself being dragged in to meetings to write roadmaps, estimate schedules, and contribute paragraphs to the annual budgeting process, you know you're on the right track.
He does have one thing right, that this is about reputation, because you cannot just go out and unilaterally take this authority. It has to be earned. Having a large number of lines of code written, commits landed, and tickets closed can be a means to that end, but it is not in and of itself the goal.