It didn't work for me on Linux with newer Wine versions, but I could launch the game with this Lutris version of Wine 7.1 (downloaded from here: https://github.com/lutris/wine/releases/tag/lutris-7.1). Just download and unpack wine-lutris-7.1-x86_64.tar.xz, go to the "bin" directory, and launch the game with:
./wine PATH_TO_GAME_DIR/Windows/LastDays.exe
(Of course, you should write the correct path to this game's directory instead of PATH_TO_GAME_DIR)
Edit: I installed the required Visual C++ runtime of course.