It's not instead of central currency, but in addition to it.
The advantage is that businesses can transact with less conventional liquidity so they don't have to rely on bank loans. This allows them to charge less to customers who use the local currency.
In the long term, this makes money [in general -- both kinds] move slightly faster within the local market, which makes the money [both kinds] more valuable [within the community]. And since the money [again, both kinds] is staying in the local market, the community's wealth is less likely to be drained by external speculators.
I think Rushkoff's notion was that new local currencies would be in addition to central currency. It just allows businesses to give a discount to transactions that will keep the wealth inside the community.
It's a neat idea, I just don't know how you would protect it from financial services turning it into yet another abstract tradable asset that undermines the original purpose.