I can't read this article but I've seen this data before and the argument that
accompanies it, here:

https://ourworldindata.org/land-use-diets

But there's a bunch of problems with the argument. First, it's obvious from the
graphs that we can save pretty much the same amount of land if everyone switched
to a lacto-ovo-pescaterian diet, rather than a strict vegan diet. The difference
in emission reductions between the two diets is 2%.

Second, as others have pointed out, most of the reduction in land use comes from
pasture, which is not always useful for agriculture. This is not as clear cut as
either side on this debate may think. On the one hand, much pastureland was
created by humans in older times who deforested large areas precisely to raise
their cattle. For example, this is the case in much of North-Western Europe. On
the other hand there are vast areas of the Earth that are not naturally covered
in forsts- think of the steppes, for instance. How much of that land should, or
even can be returned to trees is not clear. Some part of it will remain whether
we want it or not, simply because forests can't grow everywhere on Earth.
There's no reason not to use such land for pasture.

Third, as the ourworldindata.org article makes it clear, it's not just calories
and amount of proteins that matters in nutrition, but also the quality of
protein, micronutrients and minerals. Some of these, namely B12 vitamin, cannot
be obtained from plant sources and must be supplemented in the diets of anyone
going vegan. So "if everyone were vegan, only a quareter of current farmland
would be needed" plus many hundred times the current amount of supplements of
B12 and other nutrients. The costs of supplementing the entire population of
Earth with at the very least B12 is not often discussed but it is an important
question: if everyone goes vegan what will be the cost of ensuring nobody goes
malnourished as a result?

Yet another observation is that not all dairy production comes from cow milk. In
large parts of the world, for example all around the Mediterrannean and in large
swathes of Asia, dairy comes primarily from small ruminants, sheep and goats,
and some of those places also happen to occupy natural pastureland (again, think
of the steppes). There's no reason not to consume dairy from small ruminants
raised on such pastureland.

There is a common misconception that I see in discussions like this, that
emissions from farming come from "cow burps" (sometimes people say "cow farts").
As a matter of fact, cows, like all animals, cannot produce new carbon gasses,
like CO₂ and methane. They can only return to the environment what they take
from the environment: plants bind CO₂ from the atmosphere, animals take the CO₂
from plants and other animals and then they release it back to the atmosphere.
So these emissions cannot add new carbon to the atmosphere, they are part of the
natural atmospheric carbon cycle and they are not normally counted towards the
increase in CO₂ and methane levels in the atmosphere.

So what causes all the emissions from the agricultural sector? That's land use
change. Which means, cutting down forest and replacing it with cropland, be it
for human or animal feed. Because forests bind large amounts of carbon in plant
tissues, when trees are cut down and not replaced with new trees, but crops that
don't have the same capacity to bind carbon, a large amount of carbon ends up in
the atmosphere with nowhere to go. And that is the principal contribution to
greenhouse gas emissions by agriculture.

Finally, and lest we forget: emissions from agriculture are the minor
contributor to climate change. The major contributor is burning fossil fuels.
Three quarters of greenhouse gas emissions are caused by burning fossil fuels.
Burning fossil fuels, not farming or agriculture, is the cause of climate
change. Fossil fuels bind carbon over millions of years and we have released a
gigantic amount of it within a mere 200 years. Reducing fossil fuel burning is
the primary target for greenhouse gas emission reductions- not food.

https://ourworldindata.org/emissions-by-sector