This is caused by a rotation of the model (90 degrees on the X axis), as you can see in the picture you posted here:
If the object was "unrotated", so to speak, it would be oriented with the car's length along the Z axis, rather than the Y axis.
You can see this by clearing rotation (AltR), or just typing in "0" in the X rotation box.
The object dimensions reflect the unrotated object, which is why the largest dimenions of your car in the Z axis, rather than Y.
To fix this, instead of clearing rotation, apply the rotation (this will make the current rotation the "zero state", and the dimensions will be calculated accordingly). To do this, press: CtrlA to open the "Apply Transformations" menu, then choose
Why this happened:
As you know, blender uses a Z up axis system, as is more common in Math.
However, many other 3D apps use a Y up axis system which might be more intuitive to laypeople, who are used to only 2D axis systems (where Y is the "up-down" axis).
OBJ files are also normally saved with Y-up coordinates. So when Blender imports OBJ files, it automatically rotates them by 90 degrees along the X axis so that they will be oriented correctly within Blender.
Since the people who wrote the OBJ importer didn't know for sure whether users will always like this (I assume), they did not apply the rotation.
Which is why objects imported from OBJ files are always initially rotated by 90 degrees in X, and their dimensions reflect this.