The slang expression se les bouffer can be used with two meanings.

In the first one, les means the others, the opponent:

Les anglais, on va se les bouffer.

That means we are going to strongly defeat them, to crush them, figuratively to eat them the cannibal way.

The second one is when you realize you made a big mistake or that you lost something, you reached a non return point so there is nothing to do. You are then alone and ruminate the past. Here les means a couple of personal items sometimes called les bijoux de familles…

In your sentence, the second meaning is used. C’est à se les bouffer means that the situation is so disappointing that there is no hope, the person is upset and has nothing to do outside meditating and settling his nerves.