Note that the passage excised from "Against Interpretation" actually comprises the first part of a larger statement. In it, Sontag points towards an evolution within how art has been experienced by humanity, thanks to the schools of interpretation originally introduced by the ancient Greeks.
For Sontag, at least, a lot of art's magic has been lost due to modern culture's insistence on analyzing and evaluating it, breaking it down layer by layer to reach its hidden meanings. She understands this as a primarily destructive process, one that actually reduces the value of art by removing much of its potency and impact. This effect is all the more severe, Sontag suggests, given the effects of modernity, and the degree to which human beings have collectively become insulated within the mechanical, industrial world.
For Sontag, this connection between art, magic, and spirituality, is based in the immediate, visceral impact of the work in question. This is a connection void of any intellectual foundation: indeed, for Sontag, the moment you submit a work to formal analysis and interpretation, its power has been lost. Art must be experienced if it is to be alive. With this in mind, I would suggest that this same viewpoint might be tied into any explanation concerning the link between art and spirituality, given that spirituality itself tends to be first-and-foremost experiential, and that religious music or imagery aims at creating in its viewer or listener an intense, experiential reaction. It is not created with the aim of being analyzed or deconstructed, it is created with the aim of producing a powerful emotional effect.