Is it possible to extract the depth data from a .obj file?
I would like to get the same depth data that are captured by the Kinect sensor
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There is no "depth" data as such in an OBJ file. An OBJ file contains a mesh made up of vertices and faces. The concept of "depth" only would play a role if you were to look at the mesh from a certain location.
So if you want to generate fake depth data, you'll have to load them mesh, set up a virtual camera, and render a depth buffer for example. Or if your mesh is particularly dense, you could interpret the vertices as a point cloud and take it from there.
Then there is a bit more to Kinect's internal depth values than just some millimetre distance, but that's perhaps a bit too much to go into.
If you are looking to store depth information from a Kinect in a file, look into converting the Kinect data to a pointcloud, which you could then store in a PCD format or something similar. (XYZ would suffice as well). If you would use something like PCL you could subsequently process the data to your heart's content.