OK, so I modified nginx and php5-fpm to talk on port 9000 and used tcpdump to see the traffic. It looks like it worked as packets arrived at 1 second intervals (the sleep(1) in my code).

However in browser it was still the same.

After more testing, it turns out there's something in my computer configuration that's causing it. Not sure yet if it's the antivirus or something else, but trying on different computer worked, as it did using lynx on the server.