The mining firms are (partly) of a huge scale because that is what is needed to succeed globally, and they have achieved the scale through very considerable international expansion (including substantial mergers - think Rio Tinto, and BHP Billiton).
As the post argues, the two big Australian retailers haven't been anywhere near as 'brave' internationally.
We seem to do well at taking tried and true business models (dig up iron ore and sell it, buy cheap fruit and veg and sell it at a big mark up) but we have a poor track record for establishing creative companies. Creative in that they create something. products/services that didn't exist before. Its kind of weird that there seem to be so few Australian tech companies that are international big players.
In terms of other large Australian companies there's also New Corp but Im not sure that dead tree publishing qualifies as an innovation based business. Plus I think they moved to the US a few years back.