Nutritionists will tell you what really matters is what type of fat/protein/carbohydrate. It's not one or the other. You need to eat plant based whole foods protein, fat and carbs too. For the most part, humans are carbohydrate processing machines (good carbs: like beans, whole grains, fruits, vegetables), these should be your staples.
That diet is good for weight loss it’s not good for overall health. Search on google scholar about “Whole food plant based diet” you will find many studies on this diet especially focusing on cardiovascular health improvements.