Do man-made machines take natural Nitrogen out of the atmosphere and in turn cause global warming?
The short answer is that using atmospheric nitrogen as a feedstock for industrial processes doesn't really affect the climate per se. It does mess with the environment (primarily through deposition of nitrogen fertiliser) but this is a separate issue. 

The problem from a climate point of view, is that the process is virtually certain to emit a lot of greenhouse gasses (primarily CO2 from fossil fuel powered machinery)