You might want to read up on what is generally considered to be an ARPG. Procedural isn’t mentioned once.
Modern ARPGs use procedural, or at least quasi-procedural methodologies, but the genre as a whole is not required to have such for the classification of ARPG. Action (realtime character control in combat) and RPG (character and/or item growth) do not require procedurality to be classified as ARPG. That’s simply a bonus of modern tech that allowed more complicated code and/or storage environments.