The JSON you pasted above is valid, but for some reason the JSON on the page isn’t. If I paste in the code above it works fine for me (in the ‘settings’ page demo map). I did this:
1. Went to settings
2. In the styled maps section I pasted the code you provided above verbatim. I gave the style the name ‘test’
3. I saved the settings
4. I selected the new map type in the ‘map types’ section and saved again
5. Now I was able to select map type ‘test’ in the demo map (and see the styles)
What happens if you follow those steps?