Which, at the scale of business they are referring to, might just be the reality. Although I also find it to be a very distasteful warping of human priorities, personally.
The Silicon Valley pattern of VC-backed startups is distinct from other patterns of new business formation. This SV pattern focusses on high-growth and high-valuation. It is specifically geared for wealth-creation. That's the primary motivation for most of the key people involved, definitely the motivation of the investors. It's a well-known fact that VC's need outsized returns for their investment model to make sense. So it's not even just making money that is the priority, it's making a lot of money. There are other more predictable ways to start and build businesses if your goal is not maximum return on investment.
So to me, when an investor says, "If you aren't going to put your startup in front of everything else in your life. It will fail," it sounds a lot like, "Making money is more important than people."
It's the difference between a priest or a nun following what they believe is their life's calling and a televangelist promising their audience blessing if only they'll sacrificially give their life savings as offering.
It's also worth pointing out that Ron Conway (as far as I can tell) was never actually a founder himself. He's not had to take his own advice. To be fair, I'm not familiar with all the details of his life, so maybe I'm mis-characterizing.
I've spent a good portion or my career working with and for startups and small businesses, so I'm not just against them on principle, but this advice, coming from this source really feels off to me in the same way that as a Christian televangelists feel disturbing and off.