I am completely new to everything electronic as well as arduino based projects. I am wanting to make a small time lapse camera that will take a picture every pre-determined interval. Is there a way to do this using the tinyduino board components?

I found a similar project online here: http://fyt227.wix.com/timelapsecamera

Could something like this be possible with the tinyduino, minus the wifi part as I do not need that function?

This looks like a feasible Tinyduino project. You will need the processor board, the SD card board (for storing images), and a 3rd party camera board. You will also need one of the proto boards to wire the camera to in order to add it to the stack. Time lapse durations could be set in the code or you could expand the project to include the Tinyscreen which has 4 buttons on it. Those you could make to change time settings and start/stop the camera as well as show last image taken.

Have fun!