"drush cron" doesn't work anymore after moving the site to a new server
The issue was fairly simple to solve. 

I had forgotten to create a settings.php for each site. I was able to find out by running the following command:

drush --local -d -r /var/www/testproject/build/html status


And from the output I was able to see:

[debug] Could not find a Drupal settings.php file at sites/default/settings.php. [0.14 sec, 10.8 MB]


That was it