From the OverDrive Library Blog:
…we’re happy to announce that browser-based audiobooks will be joining your collection in 2015 – instant access, maximum ease of use. See audiobook, play audiobook – and that’s all it takes!
All of your MP3 audiobooks will also be automatically available as browser-based audiobooks: Download using the app or listen instantly in your browser!
A 26 second promo video can be viewed here.