Both of them are not phenolic compounds they are heterocyclic compounds. Pyrone is heterocyclic chemical compounds, contains an unsaturated six-membered ring containing one oxygen atom and a ketone functional group while Kojic acid or5-Hydroxy-2-(hydroxymethyl)-4-pyrone or 2-Hydroxymethyl-5-hydroxy-γ-pyrone .
A widely accepted definition of phenolics mentions that phenolics are compounds with molecules containing aromatic ring (s) attached to hydroxyl group (s). So kojic should not be classified as a phenolic compound.