It doesn't. It has a code generator in its SDK that allows Android developers to recompile their apps for the BB and release it on the BB App World.
There's no reliance on BES/BIS in BB10. It actually supports more e-mail standards than Windows Phone, including AS and the dreaded CalDAV/CardDAV.
The future of BIS/BES is as software for IT managers to manage BlackBerry, Android, iOS and Windows Phone devices across the enterprise. They've redesigned it for the BYOD universe, and I expect they'll see a lot of success from that approach. No other major player (including Microsoft) can securely manage all devices across the board from a single solution.
I wouldn't count them out.