Yes, it is completely proper English and is the sort of thing that you would say but probably write in a slightly different way. If the author used punctuation properly then the sentence would be been something like this:
"“I think, universally, founders and early startup leaders underestimate how hard people-work is,” she says."
The person talking may have been using 'people-work' as a jargon term for team management, but otherwise there is nothing out of the ordinary about the statement.
Maybe it is one of those jargons used by high professions? Or maybe it's just made up to sound like one?