I’m sorry but it’s difficult for me to debug your installation.
There might be some updates in meanwhile, but I’m using this box: https://atlas.hashicorp.com/parallels/boxes/ubuntu-14.04 (v 1.0.7) with Parallels Desktop 10.2.2.
In newer versions of PD they have removed CLI from it and you need to purchase some more expensive license to get it work, this is why I stick to v10.
So depending on the versions you use there might be some additional tweaks required.
You can find some instructions on their help site: http://parallels.github.io/vagrant-parallels/ which might help you.