Not even close to pretty, I saw the same special you linked when it first aired. Yellowstone going again like that isn't a local event; it's a global event. After the immediate fallout, it would be weeks before we could even begin to accurately tally the missing and the dead, which would go into the millions. It would come down the government assessing how much of the continent is still inhabitable, and those portions of the population that can shift outward will, and the rest won't make it. Much of the US and Canadian infrastructure will grind to a halt under the ash plume, and I imagine NORAD and the SAC will go to a heightened state of alert and warm even the nukes up, in case someone out there decides to capitalize on the stunning blow North America just took.
But the ash plume will be so bad that it will tip the globe well beyond anything we're seeing with present climate change. I suspect most countries will just be hanging on to ensure that ends meet. In fact, fighting in a burning house is right up there next to stupid; you might see lots of regional fighting to get to clean water and food, including here in the States, but also I'm willing to bet it could foster unprecedented international cooperation.
Thing is, this will happen eventually; someday Yellowstone the park will be gone, but of course it also rose like a phoenix from the last one 70,000 years ago, all part of a massive cycle of destruction and renewal. Yellowstone is a curiously rare geological hotspot in the center of a continent. It might happen in our era and it might not. Of course it could still happen on a smaller scale eruption and still frack things up badly, the knowledge gained watching this thing and learning from it will be worth more than its weight in gold.