I currently use the Arduino UNO WiFi, but when I try to use the WifiChatServer example, I keep getting the same error:
wifi shield not present.
What am I doing wrong?
That example, and the library it comes with, are for the Arduino WiFi Shield. Not the Arduino Uno WiFi, which is an Arduino Uno with an ESP8266 strapped on the side through an I2C->UART converter chip.
You can't use that library, nor the examples that come with it. Instead you need to use the Uno WiFi library as stated in the FAQ for the board:
If you are using the Arduino 1.7.x then you need to use the ArduinoWiFi.h library that it is already included in the IDE. Instead you are using the Arduino 1.8.x then you need to download the UNOWiFiDev.Edition library from Library Manager.