Seems pretty straight forward - pretend you signed up for a Google account and also had that account connect to your other email addresses (Like people have been doing for years, and arguably one of gmail's best features)
Now just rebrand it without the visible requirement of having a Google Account. I wouldn't be surprised if you're still getting a Google account in the process, it's just not advertised.
When you go through the sign up flow you can select whether you want to Gmailify your address into an existing or a new Google account. We make it very explicit that all your mails are being copied into Google servers.
By the way, while Gmail always has offered ways to just "import" your messages from a third party address, with Gmailify you get a full two way sync, so you can e.g. keep using the Yahoo UI and your changes will show up in Gmail.
I do not seem to have the option to gmailify my address. Is the feature restricted to specific providers? If yes, are there any plans to support Office365 addresses?
Now just rebrand it without the visible requirement of having a Google Account. I wouldn't be surprised if you're still getting a Google account in the process, it's just not advertised.