There seems to be issues with how mouse input is grabbed by TGE under wine, like the mouse input buffering doesn't work correctly anymore. If you're getting less than about ~80fps you'll start noticing mouse input issues due to the inputs being ignored between frames, so you should disable vsync so that it's possible to get the higher framerate and thus get enough frames to consistently have your mouse inputs picked up.
That aside, another thing that can help is disabling mouse acceleration. In Gnome you can disable mouse acceleration by opening gnome-tweak-tool (you might have to install it through apt first), and then switching the mouse acceleration profile to 'flat' under the keyboard and mouse settings.
