It seems like for Gmail to provide this functionality, it needs to copy your external email to Google's servers and do server side processing.
I can't imagine that it does spam protection, Google Now cards, and search all client side.
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.
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.