Well, first off I'd be somewhat skeptical of the data. The person who put the chart together is an artist (not a social scientist or an art historian) who normally makes charts of data that's easily looked up and compared (tallest planned buildings, most subscribed Youtube channels over time), historical maps, and creative/projected maps that don't require real data. This is a big step outside of what he's used to. He claims to have looked at over a thousand images, but what does that really mean? Does that mean that he looked at 300 for southern Europe, 400 for northwestern Europe, 50 for North America, 100 for China, and another 50 for the "Arab realm"? That would mean that some of his percentages were much more accurate than others, and "several dozen" depictions per era is really not that many in the first place for drawing conclusions. Also, was Native American and Islamic art (the latter of which does not depict humans until partway through this chart) actually a significant part of his data, or did he estimate without admitting to it?

Another issue is that these are not all separate cultures. If the areas where Vargic concentrated his data with, say, southern Europe followed the areas where more art was produced (Greece, then Rome, etc.), a change in the proportion of facial hair could be more a result of a different culture than time. I'm not saying that this in necessarily what the chart reflects, but you don't want to be too trusting with data that comes from one person's study of a multi-century period, especially when they don't have experience in it. Another consideration is the multitude of religious art from the Middle Ages and Renaissance - is he making allowances for religious figures being traditionally depicted with facial hair (or without it) or is he counting them in his totals? This is where I'm skeptical of that convergence of southern and northwestern Europe around the time of the Renaissance, because the Renaissance saw more straightforward portraiture to balance out the John the Baptists etc.

Nitpick:

For 2,000 years, North America had the fewest number of men with facial hair. But around mid 18th century, we see a huge jump from about 10% of men having facial hair to over 90%.

This really threw me, and originally I was going to write about how the chart is Wrong, All Wrong, but when I looked closer the trouble is that the article writer can't read charts. From 1750-1800, there's a rise up to 30%, which is followed by the spike of the 19th century. There is no sudden mid-18th century spike. There is a gradual increase (partially attributable to increased European immigration) over about a century.

If you want to read about the 19th and 20th century changes, there are good answers here and here.