I believe that Saiga rifles are a derivative of the AK, not a variant of the AK. Variants of the AK include modified Saigas, as well as the AKs made by numerous non-Russian countries (ex. Bulgaria, Finland, Yugoslavia, China, etc.)
The new law prohibits Saiga shotguns by name. However, the law is silent as to the rifles. Therefore, it appears to me that the failure to mention Saiga rifles by name was not an oversight.
The FAQ from the New York State Safe Act website makes it clear that absent an express prohibition by name, the definition of an “assault weapon” is based upon feature