Never mind. I found it 🙂
In another question somebody asked for the blend file from which the example was rendered, and Kent provided the blend file.
I compared the settings there with my file (only the nightstand lamps), and found the difference that made the lamps shades bloom more.
In the properties-panel / Scene tab / Color management – the View drop down is set to ‘Filmic‘. Set that to ‘Default‘, and there’s the bloom on the lamp shade’s.
This ‘filmic’ was introduced in blender 2.79, so it wasn’t in the version that the tutorial was made with.
