How can I embed a view in an email sent by Rules without resorting to the PHP filter?
Using Insert View, Mime Mail and Mail System module, you can send views in emails.
After installing and enabling the above modules, you will need to configure Mail System settings and Text Format settings.  


In the Mail System settings,
Change all settings to use MimeMailSystem class to send mails.
Note: Site-wide default MailSystemInterface class should be MimeMailSystem.  
In the text formats settings,
Enable Insert View Filter in each text format you require.


The problem for you isn't with the rules. It should be the Mail System settings.
I hope this would work.