Well, these kind of things make me hungry.

The ssh alias can not understand the tilde ~ character.
I have a line similar to this in ~/.wp-cli/config.yml:

ssh: dh-k1
  path: ~/sites/example.com/www

resulting error:
Error: This does not seem to be a WordPress installation.

when I change the config to

ssh: dh-k1
  path: /home/user/sites/example.com/www

everything works.