They aren't trading possession on the blockchain in most cases. Generally, the BTC is in an exchange's wallet and the exchange maintains the accounts of the traders until the traders withdraw their assets.

edit: Some cross exchange trades (i.e. buy BTC on one exchange and sell on another) would still require a move across the chain, but it all really depends on what the exact mechanics of the trade are.

Note: the article confuses two distinct things wth each other, or at least makes it unclear: the transaction volume that is allegedly dominated by high-speed traders is in the forex market, with people trading a promise to e.g. USD, EUR and Yuan for a promise to bitcoins.

Only when someone withdraws his Bitcoin promise does it become a transaction on the blockchain. Until then it's just an exchange saying it owes you a certain amount of bitcoins. This becomes evident when an exchange defaults on this promise because of e.g. a hack, as has been the case with Mt. Gox, Bitfinex, Bitfloor and many others.