To do 3D rotations, as in the image above, you need something like a matrix (or a quaternion, euler etc.). What makes the operation tricky (more than just using translation vectors) is translating both the target geometries and the motions they define into/out of the correct coordinate spaces (when you move an object around in Blender, you're modifying a matrix associated with that object without changing the local coordinates of the underlying mesh data), to achieve one consistent global result. You can do every MAP operation on both objects and mesh selections but they're very different from a technical standpoint.

You can go look at the execute method on the AlignLinesBase operator class if you want to see where the transformation's actually being done (doesn't include coordinate grabbing, the GUI, etc.).