And how is the author instituting this knowledge culturally at work?

The implied equation of sleep and vacation is far too crude. Mixed in the post is the golden nugget that it's necessary not to burn out. Vacation is simply one very specific way to account for that, and probably not even the best. I'd say a much more effective way is to make realistic expectations of team members and yourself, such that no one is being over-worked for indefinite periods. That is much more culturally advantageous. But I do acknowledge the difficulty of instituting that in a startup, what with its bursty nature of stress and periods of slack, so vacation might be more appropriate there then elsewhere.

That's not to say vacation isn't important. It definitely is. Just not as the primary defense against burnout.