I did try your terminal command, Sleeper12, after I'd already used the Remove option from the Software Manager. I figured it couldn't hurt!
Now, an amazing addendum... I rebooted one more time, and the wine-wine remnant has now vanished from the Menu Editor! Hooray!!!
(I am using entirely too many exclamation marks.)
So this is [FULLY-SOLVED] now. ...Nah, I won't go back and edit the title.
I thought the term "wine bottle" was a pretty clever way to label a reserved folder or directory for Wine. One of the fun things about learning a new OS is collecting a whole new list of jargon. Linux programmers seem to have creative imaginations when it comes to naming things.

I guess someone is probably already thinking of labeling their bottle directories with titles like Ripple and Zinfandel and Sauvignon Blanc....
Cheers!