Sodium cyanide is classified as an inorganic compound for historic reasons, much like the entire organic-inorganic classification system is historical in reasoning.
The basic initial idea was that forming organic compounds required a vis vitalis, a life force, and could therefore only occur in living systems. On the other side, inorganic compounds were easily synthesised in vitro and have been synthesised even before alchemy was renamed to chemistry. These included most ionic compounds then known.
Naturally, sodium cyanaide is ionic. Most notably, early chemists would have been able to precipitate cyanide from other cyanide sources, redissolve it and add a sodium source (most likely sodium hydroxide) to regain sodium cyanide; thereby classifying it as inorganic.
In 1828, Friedrich Wöhler disproved the vis vitalis assumption and laid the foundation for synthetic organic chemistry. Yet the distinction between inorganic and organic chemistry was still upheld. Rather than defining it by synthesisability, it was said that any molecule containing carbon be organic — or one of many other similar definitions. This could exclude the cyanide salts but does not have to. The only salts and carbon-containing molecules that are always and consistently classified as inorganic are carbon monoxide, carbon dioxide and (hydrogen)carbonates.
By now, the distinction between organic and inorganic chemistry has lost most of its relevance and is only there for historic reasons. In principle, the distinction is that organic chemists are more interested in the carbon-containing compounds while inorganic chemists lean towards other elements more. But then there are numerous in-between fields that don’t really fit anywhere such as organometallic chemistry, bioinorganic chemistry etc.
Therefore, treat the organic/inorganic distinction as a historical residue and don’t read anything into it.