The idea of the vegan diet being "good for humanity" isn't solely about land use which this article focuses on. It's mostly about use of energy. Vegan diet: food from land -> truck -> grocery store -> my mouth. Meat/dairy/what have you: food from land -> truck -> animal's mouth -> truck -> grocery store -> my mouth. And when it comes to meat it means years feeding and water etc. until the product can actually be sent…
Rather than breaking things down by meat or plant, we should just be looking at cost per calorie.
There are classes of plants which use much less resources than meat to produce a single calorie. These are generally grains, potatoes, and anything which produces edible oils (olive oil, canola oil, etc.)
There are also classes of plants which require much more resources than meat to produce a single calorie. Generally speaking, all fruits and vegetables, especially leafy greens (which are an order of magnitude more expensive per calorie than meat).
So, veganism or vegetarianism are not necessarily good for the environment. If you switch to being a vegan/vegetarian, but your grocery bill stays the same, then you environmental impact is probably about the same.