The dude grabbed a jar of calm liquid with no steam coming off of it. He had no reason to wear gloves just as you have no reason to wear oven mittens when you eat dinner. The plate is either no longer hot or the chef was wearing them as a precaution against splatter.
Obviously liquid pouring out of a hose might call for different precautionary measures then a dude holding a cup that's not even as hot as McDonald's coffee.