OK I managed to figure out the problem with Skyshine's BEDLAM and its Options menu not closing.
Game: Skyshine's BEDLAM Redux
Installer MD5: 9FA7FDB957941EB0B9E6B53F6A9EA4A3 setup_skyshines_bedlam_redux_2.0.0.2.exe
30CDB581D87CC26574C5BBB935E897FA setup_skyshines_bedlam_redux_2.0.0.2-1.bin
WineHQ AppDB link:https://appdb.winehq.org/objectManager.php?sClass=application&iId=17120 Distro: Antergos 64-bit
Kernel version: 4.5.4-1
Graphics card: Nvidia GeForce GTX 560Ti
Graphics driver & version: Proprietary 364.19
Wine version(s) tested: Wine 1.9.9
Install notes: Install and disable ALL xinput DLLs in winecfg for the game.
How well does it run: Almost perfect. You may experience the sound just cutting out completely until you exit the game and start it up again
Details: I played as the Mutants and as Humans before dying twice to some random thing or another. I fought at least 10-15 battles and everything worked.
For those of you who see the Options menu right when you start the game via Wine, open up winecfg, add the Skyline's Bedlam executable, and set all 4 xinput DLL files to "disabled" in order to get rid of the issue where the Options menu will not go away.
I had the sound drop put on me once just after the intro where some guy was sending out my character to go out into the wasteland towards Aztec City. I did skip the intro entirely in another playthrough and the music seemed to work fine throughout my time with the game.