Two things:

One: It does not work with the default install directory selected. Z:\Games\xyz maps to /Games/xyz which you do not have permission to write. Install to C:\Games\xyz and the game will land in the drive_c folder of the active wine prefix (it is a good idea to use a separate WINEPREFIX for each game / program, so you can tweak WINE's settings individually, but this is not necessary. The default is ~/.wine)

Two: I need to run the installer in a virtual desktop. Run winecfg, go to Graphics, enable "Emulate a virtual desktop." This can be disabled after installing the game.

It's been a while since I fiddled with these, but setting the compatibility mode to Windows XP might have helped too. I'm testing one now (Dark Souls 3) and only the first two steps were necessary.