Having a control group without a diet plan would have been stupid. It would not have helped resolve the hypothesis (that fitness trackers help people lose more weight than the traditional self-monitoring of diet and exercise), and it would have reduced the power of the experiment by reducing the group sizes.
Why do you think the exercise goals were different for the two groups in this study? The "Physical Activity" section of the paper does not describe any difference in the prescribed regimen -- only, as I remarked above, on the method used to measure and record their exercise (and diet). As far as I can tell, you're flat wrong about the number of free variables.
You're already in a hole. Stop digging it deeper.