How to run my IDUINO Yun Shields stand-alone?
Yes, you can. All you need do is provide it with a regulated 5V supply on the 5V pin and it should power up and boot.

There's not a lot of IO on it though, so connecting to sensors and such would be hard, which is where the Arduino comes in handy. You communicate using the UART, so any microcontroller with a UART can be connected to it.