Is it important to maintain a work-life balance as a PhD student?
It is very important that work-life balance be available to people who need it.  Most PhD students and most scientists need some form of balance but exact needs vary.
You are not obligated to adopt someone else's idea of balance.  There is no evidence that what works for other people will work for you.
Healthy diet and exercise are strongly correlated with better health and longer lifespan.  There is very likely a causal relationship there.  But I don't think that's what you were asking.

Would you consider the cultivation of a field completely unrelated to your own to be an essential component to an academic career?

No.  Common, normal, and fair, but not necessarily essential.

being human in general?

That's more of a religious question than an academic question.