All Wordpress one-click droplets hshould ave Postfix, a mail server/MTA, installed. You can verify that it’s running by looking at the output of:
sudo ps wwaux | grep postfix | grep -v grep
Try running the following command on your droplet:
nc -z smtp.gmail.com 25
If it does not output the following, it’s possible that SMTP is blocked on your droplet. In that case, please file a support ticket and the support team will take care of it. Thanks!
Connection to smtp.gmail.com port 25 [tcp/smtp] succeeded!
Let me know how it goes.