No they can't. The construction crew - which includes the manager - can say that they built a skyscraper.
If the construction manager did lay the bricks or did the majority of the work in all aspects, they could claim to have built a building. Otherwise they contributed work, no denying that, but they can't claim credit for building it. Same way that architects can't claim they built the skyscraper, even though they probably spent a lot of effort designing it to specs. To the best of my knowledge, no serious architect claims they "built" the building. They have designed it yes. Same way, the construction manager would claim they have managed the construction.
I admit that the classification is fuzzy, but there's an explosion of vibe coders going about claiming to have built things, whose contribution is basically spending a total of one hour with a prompt and and LLM doing basically all the heavy lifting.
That's not necessarily the case of the author here, but the line has blurred a lot and people very giddily claim credit for much less actual accomplishment than what would've flown in the past.