It mostly is, but the author asserts that the advice is also applicable to (the minority of?) people with other goals.
The author deals with the question of the advice recipient's goals near the start of the piece:
> For some people it means finding work they love. For others it’s about meaning. For many it’s just getting promoted. Still, here’s what I usually say.
The rest of the piece does sound like corporate ladder-climber advice. For example:
> [...] and people notice. That’s enough for a while. But eventually it’s not. Everyone around you is technically strong too. So for most of us, you won’t stand out anymore. You need to increase your impact in other ways. [...]
Where, to a ladder-climber, "impact" is corporate euphemism for recognition and promotion ("people notice" and "stand[ing] out").
And common corporate getting-recognition advice:
> And do it in the open. A common mistake is assuming work speaks for itself. It rarely does.
And even the closing words could be constructive advice for ladder-climbers:
> And in the long run, the best way to get what you want is to deserve it.
But it could also be applicable to the rare/mythical unicorns who just want to do good work within a corporate environment.
I don't think those points have to be interpreted as promotion-seeking advice. Even once you have attained a position of where you are doing work with impact, that you find meaningful, work that you love, or whatever else it is that motivates you, you still have to maintain that position. In some ways, that is harder to do than seeking out a promotion since the person who replaces your boss may not understand your role or may not even understand why you are not seeking a promotion. Even if the people around you remain the same, they may take you for granted.
True, it also applies to people who want to maintain their position, not climb higher. (At least in orgs that don't have "up or out" culture.)