I fixed this after much searching. I guessed the solution.
I had the same problem (
"You have updates available for other accounts.
To update this application, sign in to the account you used to purchase it."
I suspect that in some instances the App store Apps become associated with a specific user account (as in user on computer not AppStore account). Or as once happened to me the same user account on a different computer, but renamed (I altered the case).
To download Apps I've purchased but can't update due to this problem I simply login to one of my other user accounts (as one does at the computers startup login screen -the screen with a row of user icons at startup). Then open the AppStore and signin using my AppleId (I only have one) then install the "Purchased" App.
When I go back to my primary user account the App has been updated and works..
Note for this to work, you may have to dele the old version from your Applications folder.. Sometimes, but only sometimes, simply deleting the app is sufficient to allow reinstallation without switching to a different user.
Weird but that's the AppStore for you. Pity Apple fails to provide proper AppStore support. Sometimes it feels as though Apple is suffering profit overload, and forgot to employ enough key staff to ensure that "It just works.", or support customers when services they've paid for (e.g., AppStore, iCloud, Safari, TomeCapsule etc) fail.