Your rect light is pretty weak compared to the lights in your example photo. How does it look with increased strenght?
However, you probably will run into trouble with so many small lights, if they are so close together. I kinda rebuilt your scene and placed some rect lights, and almost all got a crossed out icon, because too many lights in a certain radius (they still enlightened the scene way better than your test, so not sure, what this icon means, but it def have a meaning ^.^)
So maybe retry it with fewer but bigger lights, or throw in some cubes with emissive materials.
Got pretty good results with that, but again, Lumen requires objects with emissive materials to be above a certain minimum size, or they will be ignored by Lumen, and will only work for the fallback screen space stuff.
Test video, with just emissive blocks, all rect lights were disabled (also notice, how far away blocks get ignored too and light-wise pop into existence, if you get closer):
This is a standard Lumen scene, no raytracing involved.
Edit: Just for completion, i did another test, where i positioned rect lights right below each emissive mesh, and made them as big as the cubes are. then just some balancing between their brightness and the intensity of the emissive material, and you get really nice looking results 
The rect lights give you all the sharper shadows, that Lumen fail to create with emissive materials, while also hiding that popping in effect, if an emissive block is too far away.
On the other hand, the emissive blocks cover some stuff in close ups, where the rect lights fail, most noticeable at the light at the ramp.
So i would say, with a combination of those both (fewer and bigger lights overall), you should get really good results.
Also, that crossed out icon didn´t matter and vanished, once i set all rect lights to moveable. It seems to be an indicator for light baking and static lights, which we don´t use with Lumen.
Have a hopefully enlightened day ^.^