You will have a hard time saturating a 1Gbps connection with any mainstream, Flash speed test like speedtest.net. Try downloading some very large files from a CDN network or well-connected hosting company, but keep in mind you're generally going to be able to download data faster than most servers are going to be able to deliver it to you.
It looks like he's running this test from a hosting company's network (ServerBeach). However, it's worth noting that a few very lucky cities in the U.S., like Chattanooga, TN, have private 1Gbps fiber connections available for $359 a month.