Hemingway's story can be read as having an existentialist theme that life has no prescribed meaning and is not directed by a divine force. Any meaning that our lives have is a product of our own efforts.
The old man drinks in the cafe to cope with his own existential fears. Though he interacts with others only minimally, he prefers to drink in a public place rather than at home by himself. His characterization (of civility and dignity) reinforces this idea:
The old man stood up, slowly counted the saucers, took a leather coin purse from his pocket and paid for the drinks, leaving half a peseta tip. The waiter watched him go down the street, a very old man walking unsteadily but with dignity.
The contrasting characterizations of the two waiters demonstrate how they bring meaning to their own lives. The young waiter is in a hurry to get home to his wife; the other waiter, who is older, is unhurried and obviously feels sympathy for the old man. His interior monologue about "nada" demonstrates that he understands that life on its own is nothing. To the older waiter, showing the old man kindness or sympathy is meaningful.
The setting of a "clean, well-lighted place" is impersonal; it can only become a symbol of something more than that if its patrons deem it so.