I really don’t know about this band. But I was asked to answer so I watched the video and read the lyrics. The lyrics are more nihilistic than existentialist. Strange to say but Existentialism is about hope, at least Sartre’s version of it because it contends that each of us has absolute freedom to be who we are in a world without meaning. Nihilism is on the other hand about the loss of meaning. So Existentialism is a reaction to the nihilism inherent in the Western worldview.
Since the question has been brought up this is a good time to consider this duality between existentialism and nihilism. Nihilism results in alienation and anomie. This is because the world that we are caught up in, find ourselves sooner or later is realized to be inauthentic and a sham. This is especially true of youth when they realize the conventions of ordinary middle class society is not what they thought it was when they look under the surface. I tend to go back to the first use of the term which was in Turgenev’s Fathers and Sons (http://en.wikipedia.org/wiki/Fathers_and_Sons) where there is a young man who believes in Science and does not believe in the traditional mores of society. This is seen as very destructive of society by the older characters. But eventually this was radicalized by Nietzsche in to the idea that all truth is merely a lie. The basic problem was eventually seen to be with Being itself, and Existence was a concept that was not overloaded so it became the center of attention for authors like Kierkegaard, Dostoevsky, Sartre, Heidegger and other modern philosophers especially after World War II when after two World wars there was disillusionment with our claims of civilization. Given the number of wars worldwide since then and the threat of nuclear holocaust and the Cold War this view has only continued to intensify. Each generation discovers this anew for themselves as nihilism increases.
But Existentialism at least as seen by Sartre was thought to be an antidote for this. In other words if you realize that everything is meaningless and that alienation is the rule, then there is nothing to tie you to a given interpretation of the world, and therefore you are free to remake yourself as you see fit and manufacture meaning in your own life. Since Nihilism is directly related to Being, it is felt that by stepping outside of the influence of Being it might be possible to reverse the essence precedes existence orientation and instead realize that existence precedes essence. It merely says that you have to exist before you can be something. It recognizes that existence is more basic than Being. I have recounted the relation between Being and Existence in other posts. So I won’g recount that again here.
It is easy for youth to feel hopeless once they realize that the world they are in is inauthentic and conventional, and there seems to be no way out. However, this is extremely unfortunate for them and for society, and this feeling is picked up and amplified by the media, and songs like this.
So what is the answer. It is unfortunate that rebellion of youth is almost always negative and self destructive. It is possible also to rebel positively, i.e. by tenaciously and with perseverance doing what you can to change your world, even though that is for most of us close to impossible. Yet the valiant attempt produces a life worth living and meaning in ones life, and virtue, i.e. the opposite of Nihilism. Early on Nietzsche called these people Free Spirits, that is people who create their own values. There are people who do this and they are usually called Activists. And of course these activists, like Greg Mortinson (http://www.threecupsoftea.com/) for instance, all pick something different to change in the world, and set about it single handedly and dedicate their lives to the effort. So the variety of the attempts to change things is bewildering, and most fail to change anything at all, but their cause, what ever it is keeps them going in the face of the disaster that is the world and also generates meaning for others in the face of nihilism.
But how do we get youth to rebel in a positive way rather than a negative way, when each person is isolated in their own world with family, school, friends and where what society is pushing is alcohol, drugs, mindless entertainment, negative messages in music and pop culture about the meaninglessness of life, and how suicide is the only out like the example given here in this question. Occupy Wallstreet seems to be an answer. It was just an idea that came out of nowhere and caught on. Perhaps we can move on from occupying the empty places in our society adjacent to the centers of power and injustice, to actually dwelling in the world in a way that transforms it. This thing normally fizzles out, but it is almost enough to give us hope that the transformative power of youth rebellion might be brought to bear on our most pressing problems, and at the same time generate meaning to counter the pervasive nihilism in youth culture.
TS Eliot said it all in the Wasteland concerning the nihilism we are experiencing in the world. But then he wrote Four Quartets that searches for an answer to that despair. We all need to write our own Four Quartets, where we reach back into our own history for the resources to go on in the face of the pervasive nihilism we experience to create our own meaning as free spirits and to weave that together with the meaning created by others until the fabric gives us a world worth living in so that dreams of suicide are not our best moments.