Hi, and welcome
It's true the Arduino is not fast enough to do video processing (or even to stream decent quality audio in fact) however in this case the Arduino can control the shield without the data actually passing through it.
From the page you linked to:
On the other hand there is a bunch of actions can be made directly from the 3G module without having to go through the Arduino microcontroller. This means you will control all the action from the main program running in Arduino although the data may flow from the 3G module to the SD card or from the video camera to the 3G module without going through the UART avoiding a possible bottle neck and ensuring maximum speed performance given by your 3G carrier (~7.2Mbps download, ~5.5Mbps upload at max). Some of this independent actions include:
- Uploading and downloading files to HTTP and FTP servers directly from or to the SD
- Recording and uploading video and photos to the Internet using the video camera connected directly to the module
- Recording ambient audio and sending to a web server
So, for the application you're thinking of it could be possible though I didn't read enough to determine if the camera could be motion-triggered.
But let's say it's not, by adding a simple motion detector under the camera that the Arduino can use to detect movement, it appears the Arduino could then trigger the camera to start streaming through this shield to a website, or to the SD for later upload.
Don't know the shield so I can't vouch for any of their claims...
Cheers ! Geoff