This quote is said by the younger waiter to the older waiter, refering to the drunk, old man that is drinking in the cafe and seemingly refusing to leave. As always, with such questions, it is vital to look at the context of the quote to discover its meaning. This is actually the middle of three sentences that the younger waiter says to his work colleague, the older waiter, after trying to not-so-subtly get the old man to leave so that he can go to bed. This is what he says, after stating that the man will stay all night:
"I'm sleepy now. I never get into bed before three o'clock. He should have killed himself last week."
The younger waiter thus says this in an annoyed tone, as his job means that he never gets to bed before three o'clock in the morning. He doesn't care about the old man and his reason for being there and cannot appreciate the loneliness and sense of despair that drives him to a clean, well-lighted place that is the opposite of the despair that characterises the old man's life and that of the older waiter too. His youth effectively blinds him to the overwhelming insignificance and terrifying existentialism of life, and thus his wish that the old man had killed himself reflects his own selfish desire to go home and get to sleep. The younger waiter thus stands in contrast to both the old, drunk, man, and the older waiter, who is able to understand the old man's position, as he shares it himself.