The only thing that needs a blockchain is money: Bitcoin. Just use a centralized database wrapped in a publically queryable API for transparency or something for game items. There is nothing solved by putting game items on a 'blockcain'. You don't own the items. There is still another entity controlling 'the blockchain'. It doesn't prevent the gaming company from inflating the supply. It doesn't prevent the gaming company from rejecting your 'ownership'.

If whatever is tokenized is not native to the 'blockchain' it has a single point of failure: the entity that tokenizes needs to be trusted.

Just use a centrized database, it's much simpler.