Suggesting that a U.S. civil war would prompt immediate territorial aggression from other states? That's a bit of a stretch, but it's not completely implausible. Honestly, though, I'd be intensely concerned for our nuclear stockpile in such an event, as someone else said.
"It's Occam's Shuriken! If the answer is elusive, never rule out ninjas!"You would also have to worry about (and potentially intervene to secure) several other things.
For example, the food production of the US. Were a (second) Civil War to erupt here, regardless of cause or combatants, it would disrupt the agricultural exports of the US. This would cause a rather immediate and widespread global famine. The US is number 1 producer and exporter of corn, like number 2 in wheat and number 2 or 3 in rice, each key staple grains for many parts of the world. We also export tremendous amounts of meats from pork, to chicken to beef, even fish. Were a civil war to happen, all those foodstuffs would likely collapse as exports and we produce something like 30 percent of the world's food supply.
In addition we are now a net energy exporter, there are many many reserves of coal, oil, natural gas and radioisotopes for nuclear power found in the US. Exports and world supplies of those would dwindle and be cut off rapidly.
Then there's the other minerals. Gold, iron, copper, aluminum and more. We're one of the largest suppliers and producers of industrial minerals, rare earth or otherwise.
The US may be many things, but hollow and unimportant to the rest of the world in terms of resources we are not. A (second) civil war now, would almost assuredly bring about international intervention to secure all the aforementioned things. Food, fuel, minerals, all things the modern world cannot live without or with it in short supply.
Which would make a civil war a major potential flashpoint for global conflagration regardless of intervention or not. Nations won't sit idly by and let their people starve through famine, they won't let their industries dry up and halt or work diminished. Should the US be sidelined by civil war and all those foods, fuels and minerals dry up, other nations would likely begin to attack each other as well.
In simplest terms, it becomes an extremely complicated affair that can't be ignored or marginalized as something "the Americans deserved" or dramatized as having no real effect on the world outside of it. It could very much be the worst global crisis starting point in living memory.

Something i've been curious about is how would the other countries of the world react if the U.S. (for one reason or another) where to get into another civil war? I know during the civil war a few countries would help back whichever side they wanted to win but for the most part stayed out of it, nowadays everything is linked in a way that it wasn't back then.