I have "Linking Recurly Accounts with Salesforce Standard Accounts" enabled, so why didn't the Recurly account merge into the existing Salesforce account?

The Salesforce link setting of "Linking Recurly Accounts with Salesforce Standard Accounts" doesn't actually merge the Recurly account to the Salesforce account object.

Enabling this setting only creates a link between the two accounts in Salesforce, so that you can easily click back and forth between each page (the Recurly Account object and Salesforce Account object). 

You can confirm the accounts are linked by going to the Recurly Account object and looking at the field for Account --> Clicking on the name of the account. That should take you to the Salesforce Account page.