There are some important differences between your model and the sample you show.
Theirs is all rounded surfaces which makes it easy reflect the surroundings. Yours is mostly flat surfaces which have to be precisely aimed to catch reflection.
Their objects are very black which makes it easy to see reflections on it. Yours is grey, the bright surface competes with any reflections it catches.
In this quick try I deleted all the groups from "big screen" and made it all black and I dropped an "Environment Map" material on it that uses the "SparkelMap05" image.
Look at the map it uses and compare the colors on it with where they show up on your model in the render. If a highlight is too bright or the wrong color or in the wrong place in the render, you can edit the map to change it. You can switch out other maps in the material to see how they look.
You might well paint other maps to use for other objects' reflections.
This isn't real reflection, so you don't need to have Reflections on when you render unless some other model uses real reflections. It is faster than real reflection.
With more study this can be improved greatly, but this is a quick example.
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