Even though it is a synthetic chemical, DAP can be considered "organic" if it meets certain guidelines of purity and also some that are related to the sources of it's manufacturing ingredients.
Basically, it isn't but a brand of "Organic agriculture" exists for at least a century and it sells products as "better because it's natural". To be fair, DAP does little to no salting damage to soil, so it's relatively eco-friendly.
DAP (Diammonium Phosphate) is a synthetic fertilizer produced through an industrial chemical process involving the reaction of ammonia and phosphoric acid. A fertilizer might be labeled "organic DAP" if it is a blend of DAP with organic matter, such as compost or manure.
DAP contains synthetic nitrogen and is likely the most widely used mineral (non-organic) fertilizer. Therefore, it will never be approved by any reputable organic farming certification organization. Labeling it as organic is fraudulent.