I eventually got things going, but had quite a few headaches along the way. E.g. Apache was already installed, so Nginx could not bind to port 80.
I also had to install the php7 specific libraries for dom and mbstring.
The php7 fpm settings in nginx wouldn’t play along either. It couldn’t find the sock or config path. Then it had some issue with the sock file. (It’s a standard config file that you can simply remove the comments to get it going, but yes, it wouldn’t play along).