reading the specs of the shield you have, it is an ESP8266 that must communicate through AT commands with your Arduino, similar to connecting your Arduino to an ESP-01. Unfortunately, the library for such communication is not already developed. I recommend you to use the ESP8266 directly (it is possible to reprogram your shield with FTDI cable to work in an standalone mode and use the GPIO ports of the ESP8266) or purchase an ESP8266 dev board, like NodeMCU. Such boards are smaller, have more memory, frequency, and are even cheaper and provides Wifi out of the box. They can be programmed directly through the Arduino IDE and the integration with thinger.io is quite smooth.
Anyway, the library for this specific setup (Arduino + ESP8266 as Wifi bridge) is in development, so in the future it would be possible to integrate them with thinger.io easily.