mailsystem module does not appear in the selection field for HTML Mail module class
Below where you show in your screenshot, see the "New Class" field set. 
Expand that

For the Class to use for the format() (link is external) method field select HTMLMailSystem

Class to use for the mail() (link is external) method select SmtpMailSystem

Save the form. 

The new class will be available for use to set the Site Default.