The essential objective of Bitcoin Gold, as a split or hard fork from the Bitcoin chain, is to change the way the currency works. Decentralizing the issuance of new Bitcoins, allowing users to mine BTG even without possessing expensive specialized equipment.
Also, Bitcoin Gold doesn't give up on Bitcoin's classic goals. That is, facing fiat money by offering a viable alternative for its replacement. So Bitcoin Gold would claim to be the natural successor to BTC in this fight against fiat currencies.