My interpretation of the general history of warfare is that countries agree on restraint once some situation has occurred that all sides agree should never happen again. Mustard gas in WWI, nuclear weapons in WWII...
Hopefully this doesn't spiral out of control. It's not clear where the boundaries are that we don't want to cross.
In other words, whatever we would be capable of accomplishing with pen and ink on paper, and carrier pigeons, or smoke signals; that's what the internet does, but at nearly the speed of light, for volumes of data beyond anything worth attempting as a physical implementation.
In that sense, the only thing that denial of service really accomplishes for a hermit state like North Korea (which presumably attempts to censor the external internet for it's non-elite commoners already), is such that they lose face on "the world stage" where they receive no respect anyway.
The boundaries where things start to get ugly, in a new and truly modern sense, would be circumstances where autonomous weapons platforms run rampant, and inflict wide-spread death and destruction in various theaters of conflict at scales of their own choosing. I don't think that's a reality yet, at least not without a nuclear exchange. Drones, for the most part, are still essentially remote-controlled vehicles, operated by humans, particularly with respect to the decision to use force.
A scaled back version of that, which we might see emerge, before autonomous robots are used to crush a nation like it were a load of dirty laundry (or rather, before robots start to decide for themselves, which nations, or regions to crush), is infrastructure attacks that cripple things like electric and water services for extended periods, triggering cascades of famine and disease. For that to occur, a country would have to foolishly place all of its eggs in one basket, and lay prone to catastrophic failure without proper redundancies in place.
It's been spiraling out of control for years.
I'm actually quite surprised at how restrained our government has been to actually engage some of these rogue countries after decades of ongoing attacks.
At some point, you have to return fire.
And yes, I'm quite aware the US has been active in several high profile attacks. Unfortunately, it pales in comparison to what China, DPRK, and several middle eastern countries have been engaged in for much longer.
They invaded the country, and got their asses handed to them by the Chinese. The geopolitical situation is, invade NK, fight the red army.
In short, critical infrastructure all over the world is being needlessly put at risk. The operators are placing their own knives across their own throats, and all a network-based attacker would need to do is jog a few elbows.
A few people might die. It's not like anybody is putting kill-bots out there, connected to the Internet, with an easily-toggled BERSERK_RAMPAGE flag (yet), but I think water treatment plants and electrical power grids are probably vulnerable to attack, and could cause some folks at the margins to die.
If there's one thing the Sony breach and other major hacks over the last few years have illustrated, it's that there is no clear limit to the damage that can be done from something like this.
EDIT: To me, what's so frightening about this is the lack of historical precedent for conflicts between nations in the form of cyberwarfare. We don't know what could happen. We don't know if the damage will be limited to financial cost and embarrassment, and we don't know that a scuffle between nations on the Internet will remain contained as such.
People would definitely die.
Which is pretty much exactly why it won't happen.
If NK nuked Seoul, in all honesty China would probably nuke Pyongyang long before the Americans, or just send eleventy million troops across the border.
The entire reason NK exists is because China prefers a border with NK rather than a unified Korea sympathetic to US interests.
As others have pointed out, it's unclear that the US government is itself involved. Neither the attacks on Sony and the attacks on the North Korean internet links require uniquely state-owned military resources. They just require a relatively accessible set of knowledge, skills, and practical tools. We even get the term "script kiddies" from the long-running case of those with knowledge and skills creating tools that encapsulate same.
So what happens in a world where "warfare" level activities, causing significant disruption to nations and multinational corporations, are accessible to essentially random individuals? In the U.S. we might liken it to our mythology: the lawlessness of the Wild West. Yet it seems that lawlessness with this kind of ease-to-impact ratio is unprecedented.