I had no luck with the original release from 1999/2000 but was able to get the 2011 remastered version running with the following steps:-
1. Copy the whole Alice1 folder onto drive_c
2. Configure > Wine > Open a Command Prompt
4. cd Alice1\bin\
(The batch file runs 'alice.exe -RunningFromAlice2'. The tag on the end is to tell the game it isn't being opened from within Alice 2 - Madness Returns, as was normal for this release)
There are numerous graphical settings tweaks described at https://www.pcgamingwiki.com/wiki/American_McGee%27s_Alice_(2011)#cite_note-Disabled_console_and_missing_Cheshire_features-1
To make windows .bat files open in wine, it seems to be necessary to tell the text editor that "External Tools execute external commands shell scripts" (see https://askubuntu.com/questions/661113/how-to-run-a-batch-bat-file-on-ubuntu-using-wine-with-complete-steps) I don't use gedit as my text editor but the other text editor has the same option in preferences so I presume this is standard for Linux text editors. But I definitely don't want .bat files to run a executables from my file manager as the default behaviour - I only want them to do that from wine. Is that possible?