Almost everyone you know has a Gmail account. I have one as well, but the one I use is a Yahoo account. Yes, I get a lot of backlash for using an email account which is not Gmail and especially one that is Yahoo.
However, for those like me, or rather those who do not have a Gmail account to begin with, Google is making it easier for you to use the services of Gmail. What you are thinking is true, you will be able to use Gmail without even having a Gmail account!
Google has specifically mentioned that users of Yahoo and Hotmail/Outlook accounts will be able to enjoy all the privileges that come with a Gmail account. However, if you have an AOL email account, you will not be able to enjoy this service. Users will be able to use inbox filtering, spam blocking and even Google Now cards (for Android users).
Taking advantage of these features is called ‘Gmailify,’ and you will see this option in Gmail when you log in with your alternative email. Also, if you are interested to use Gmail as an email client for your Yahoo or Hotmail/Outlook accounts, you have the option of turning Gmailify off. Google has long term plans to offer this services to users of other email IDs as well so if you fall in that category, you will just need to wait it out.