Actually, I don't know the developers, but my impression has been that WINE tries its best to merge the Windows window manager with the Linux window manager, so that linux and windows apps will cooperate nicely among each other. There are limitations of course, but it's believable to me that WINE may include linux programs in the list of open windows available to Windows programs.
I have never EVER gotten the LTSpice web update to work in Linux, in any distribution. It may have worked a long time ago, but I just download the new .exe when I want to update.
