It's not about "realism" or even style, it's more about preserving detail in extreme contrast. All pixels brighter than a certain threshold become white and since there's nothing whiter than white, they're all the same with information lost. This is basically HDR (no idea why the "Filmic Color Management" phrase is necessary), as it has been common, even in real-time rendering and digital photography for years. I suppose they implemented it in a smarter way? The basic idea is to expose at different levels and combine the parts that preserve the most detail.

I don't know why they chose that scene, these ones show the difference much more: https://www.blenderguru.com/tutorials/secret-ingredient-phot...

The sRGB image might look punchier at first, but once you start looking closer you'll see it's blown out and the colours are wrong. It's like putting 10 spoonfuls of sugar in your coffee.

The real advantage of using HDR or Filmic, is that details start to show in areas with low contrast. Try looking at the window on the right or around the faucets. The higher contrast means more details are visible.

In my opinion the point is that the artist gets now better control over the end result. I think with minor parameter tweaks you could get a pretty high-contrast scene too. Also even the high-contrast render probably will look more realistic now.