The separable verb »zusammenrücken« means
to move closer
The verb »rücken« very often is used when furnitures are moved. It has no direct counterpart in English, so in English you have to use the verb "to move" (German: bewegen) instead. »Bewegen« is a more general term for movement, »rücken« is a special kind of movement. (You can't rücken things with wheels, but you can bewegen them.)
Die Kellnerin rückte die Stühle zurecht.
The waitress moved the chairs into place.
Die Möbelpacker rückten den alten Schrank von der Wand weg.
The movers moved the old cabinet away from the wall.
So, »zusammenrücken« is used when furniture is moved together:
Wenn wir beieinander sitzen wollen, müssen wir zwei oder drei Tische zusammenrücken.
If we want to sit together, we have to move two or three tables together.
But more often this verb is used when people move together:
Die, die zuerst da waren, rückten enger zusammen damit auch die Neuankömmlinge bei ihnen sein konnten.
Those who were there first moved closer together so that the newcomers could also be with them.
And from this physical movement of people derived is the figurative meaning of holding together:
Die Krise ließ die Nachbarstaaten zusammenrücken.
The crisis caused the neighboring states to move closer together.
In your quote this term is used in a mixture of the physical meaning (move closer together, so that the physical distance becomes smaller) and an ironic inversion of the figurative meaning. (They come closer together not to be friends, but to settle their conflict.)
The verb »richtig« (correctly, properly) has here more the meaning of a modal particle. Modal particles are hard to translate. Here is means, that »settling the conflict« might become a little bit harsher.