That was the low-level access. Below that they talk about porting a LWIP:

> I developed test sketches for NTP, DNS, multicast, web server, web client, httpd with SD or SdFat-beta lib, tfttp server (SD, SdFat-beta, or SPIFFS), ftpd (get/put) with SD lib, and TCP/UDP client/server

You need a TCP implementation. A few posts down shows someone using lwIP.