As I supposed, this model is used in a game. In games, rendering happens differently than in Engines like Cycles. You wouldn't put the information about the outline into the model, but code it as an effect. Here's an approach how to do this in games:
- Lock depth buffer writing
- Render the object as wireframe with a thick colored line
- Enable depth buffer writing
- Render the object again, this time normally.
There are other ways to do it, (for example with some normal calculations), but this one is fairly common.
How to recreate this effect in Blender?
Idea 1
As mentioned in the answer by @sambler, you could use freestyle.
Idea 2
Another way is to use modifiers and render passes to emulate the effects done in the game:
- Duplicate your model and put the clone on another layer. Add a Wireframe modifier to the clone and change it's material to the outline material.
- Exclude the wireframe clone's layer from your scene rendering. Add another render layer, rendering only the layer with the wireframe object.
- Composite them together with a Z Combine. Make sure the Z values of the Wireframe are always greater (farther behind) than the object, but never too far that they get hidden by other objects.

Idea 3
Another idea I found here is quite similar to 2:
- Duplicate your model. The copy will be the outline
- Select your outline model and go into edit mode
- Select all faces and use Alt+S to "extrude" them. Quit edit mode
- Assign each one a different material. You can join the meshes if you want.
- Make the outline's material transparent when front facing and black (outline color) when back facing.
The original idea used a geometry shader to extrude backfacing faces but it didn't work with displacement in Blender. Also the inner material has to be emission (I don't know why, but it is just an idea you could elaborate). Final result:

Idea 4
Similar to 2. Probably my favourite.
- Set a unique Object or material ID to the object that should have an outline (I went for object)
- Enable object (or material) render pass in your render layer.
- In compositing, use the ID mask to cut out your object. Blur the mask, color it and use alpha over nodes to put all together.
In the screenshot, I've labelled the nodes with their function so you know wich values to tweak.

Here's the node setup for idea 4: 