1.) If the Dark One succeeds at the ritual, he gains the ability to move the Gate. If he does this and moves the Gate to, say, Valhalla, then the Snarl pops out of the Gate and kills the gods on Valhalla. Then it destroys all of Valhalla until it's a big empty void-plane. And then...nothing. That's it. The Dark One does not have a way to put the Snarl back into the prison after he's unleashed it. The Snarl just lives on Valhalla now, or what's left of it.
2.) The Gate connects the prison to another plane. When the Dark One moves it, it now connects the prison to a different plane. So after the Snarl is unleashed on Plane 1, then the Dark One moves the Gate to Plane 2, it now connects the prison to Plane 2—it does not connect Planes 1 and 2.
3.) But that doesn't really matter because once the Snarl is free on any plane other than its prison, then literally any planar gateway could potentially allow it to change planes. The Dark One would cease to have any control over its location, and in fact it would be far more likely that some of the evil gods would start spamming big flashy portals to the Dark One's domain until the Snarl took the bait and went through.
4.) Alternately, once any Northern god dies, the deadlock at the Godsmoot is broken and the vote resolves (votes from dead gods don't count). Even if the world was "saved" they would be free to immediately take a second vote to destroy the world—or even just to kill all goblins—depriving the Dark One of his followers and ultimately killing him over the long term.
The Snarl is like a nuclear bomb. You can get a lot of leverage out of owning a nuclear bomb, because no one wants it dropped on them. But if everyone knows you only own one and then you use it on someone...then everyone left knows you don't have it anymore. Sucks for your one target, but it won't end well for you, either.
That's why the Dark One's actual plan is to use the threat of moving the Gate to extract concessions from the other gods and deter preemptive strikes against his followers. Those concessions will be significantly less than, "All of you be my slaves forever," because at that point, the calculus would change and some of the gods might risk the bomb getting dropped on one of them to end the Dark One's threat to their friends and family.