My local network is very basic and includes a four port hub / router with WiFi...
I've built a simple ESP8266 test board using the example WiFi client (192.168.1.5) and can access the Linux server and retrieve data using:
const char* host = "192.168.1.4";
const char* host = "192.168.1.1";
I've even created a virtual host on the windows server
NameVirtualHost esp.dev
<VirtualHost esp.dev>
DocumentRoot C:/Server-14.1VC11/data/localweb/esp/
ServerName esp.dev
</VirtualHost>
const char* host = "esp.dev";