Hi Friend,
I'm having exactly the same problem. Made a very small update to my extension yesterday and now the extension has stop working when installing from the chrome Store (works locally)
To answer your question, no you don't need to include you Key into your manifest, unless you want to create the CRX package yourself.
On my Side, I have tried rolling back and removing 9/10th of my code but the extension still won't install from the google chrome store.
weirdly that's not working either (Mac OS and Zipped from Finder and Terminal)
Please ... help us.