The numbers seems to be too much near 65535 to be a coincidence.

are you making the request from a single IP address source? are you aware of the limit of using the same source IP address for the same destination IP address ( and port )? ( each connection can have only a unique source address and source port to the destination, maxing out in source 65535 ports ) for the same destination

I wonder if that's why the cpu is idle for part of the time, it's waiting for sockets to become free.

I would expect http persistent connections (keep-alive) at these rates. It's very hard to get 64 k connections/second from a single IP to a single server ip:port without heavily tuning the client, which they don't mention doing. They're only testing for 10 seconds, but still, you'd need to clear all the closed connections out of TIME_WAIT pretty darn quick in order to re-use each port 10 times.