When I search for 'downtempo', it only shows albums, artists, and songs with the word 'downtempo'. How do I play music of the whole genre downtempo? The closest thing they have is playlists with the word 'downtempo' in it, but that is a fixed length playlist made by another user, and those playlists won't play on mobile. It just says "Cannot play station. Sorry this station cannot be started. Please try another one."
According to Spotify Moderators, they removed the genre radio feature back in 2012.
I think the closest think you can do based on what you're asking is to search for your genre (i.e. Downtempo), find a playlist that has some songs you already know, and start a radio station based off of that playlist. You can also browse genre play lists by going to the "Browse" section.