Arduino WiFi Dongle Connection
No, you will not be able to use this dongle. This device needs to be plugged into a USB Host device, which an Uno is not capable of doing for several reasons, one of which is that this dongle would require some driver on the host device, and the only drivers made for it are likely made only for Windows/Mac/Linux type operating systems.

Most of the WiFi shields communicate with Arduino over a non-USB protocol like SPI or I2C, while it looks like this dongle is a purpose-built chip that communicates with a host over USB only, not I2C or SPI.

It's likely you can find an ESP8266 device for a lower cost than this dongle would cost, however. The ESP8266 device would communicate with an Arduino via UART (serial port).