You cant have the shader only pick up specular glow from object. Postprocessing is done in a way that you render to texture from whatever the camera picks up and then postprocess this.
The only way you could have bloom based on a specular map would be to have a special render with the scene HDR-ed in a way that everything is darkened and that specular shader reflections are brightened and then after this postprocess, add this texture to bloom and then put the result on add infront of the camera. That requires 2 renders and you would still not be doing much because there may be other bright parts which are not due to the specular map. It is possible but a very hard, unfeasable, uneconomic thing to do, so i doubt they did something like this. I've never heard of it being done, and it is not needed.
In the shot where it says "specular bloom" you can see that the bloom affects the sky on the left as well as it pierces through the arches and the light spreads over the dark areas. It all looks like regular bloom to me.
The only way you could have bloom based on a specular map would be to have a special render with the scene HDR-ed in a way that everything is darkened and that specular shader reflections are brightened and then after this postprocess, add this texture to bloom and then put the result on add infront of the camera. That requires 2 renders and you would still not be doing much because there may be other bright parts which are not due to the specular map. It is possible but a very hard, unfeasable, uneconomic thing to do, so i doubt they did something like this. I've never heard of it being done, and it is not needed.
In the shot where it says "specular bloom" you can see that the bloom affects the sky on the left as well as it pierces through the arches and the light spreads over the dark areas. It all looks like regular bloom to me.