In order to log the emails sent via MassMailer as Salesforce Email Messages (HTML formatted email), first of all, make sure that you do have the 'Enhanced Email' feature enabled in Salesforce.

Go to Salesforce Setup -> Quick find 'Enhanced Email' -> Enable the same

Once that is done, go to MassMailer App -> MassMailer Setup -> Tracking Settings -> In the 'Email Event Settings' section, enable the option, 'Log Activities using Salesforce Email Message'

Once these steps are complete, the emails sent via MassMailer are logged as Salesforce Email Messages and they will appear as a properly formatted HTML content like the following: