It's difficult to explain exactly why the chapters are so short. Yound adult novels sometimes have short chapters to make them more readable. The book is clearly not a typical novel or even a novella. While not a diary, the stories are narrated by Esperanza. The eNotes discussion of style of this book is the best explanation I've found:

Just like Esperanza, whose identity isn't easy to define, critics have had difficulty classifying The House on Mango Street. Is it a collection of short stories? A novel? Essays? Autobiography? Poetry? Prose poems? The book is composed of very short, loosely organized vignettes. Each stands as a whole in and of itself, but collectively the stories culminate in a mounting progression that creates an underlying coherence; the setting remains constant, and the same characters reappear throughout the tales. Cisneros once explained: "I wanted to write stories that were a cross between poetry and fiction—I wanted to write a collection which could be read at any random point without having any knowledge of what came before or after." Despite the disjunctive nature of the stories, as they evolve, Esperanza undergoes a maturation process, and she emerges at the end showing a more courageous and forthright facade.