It might be tempting to read the story as a religious parable. Because the characters all remain unnamed (we've got the artist, the manager, and the supervisor, but no George or Mr. Kibbles) and the historical context unspecified (it happened "in the past few decades"), the story has an almost mythical quality. It might as well start "Once upon a time, there was an artist who didn't like food…" While there aren't any super obvious religious references in the text, there are details that suggest religious elements.
Perhaps the most "religious" moment is where the manager presents the artist to the public at the end of the fasting period, "as if inviting the heavens to look down at its handiwork […] this pitiable martyr" (3). A martyr, as you probably know, is a person killed for his or her religious views. Now, before we leap to assign religious significance to this act, however, we are told that "the starvation artist admittedly was" a martyr, "but in a quite different sense." The story doesn't tell us what this different sense is. In general, the story toys with religious significance only to make it harder for us to assign any moral or spiritual significance to the tale.
Want to know more about the parable-like quality of the story? Check out "Character Roles."