I have managed to get the 32bit Windows version of Doodly working in linux using wine and winetricks, and using vulkan as the renderer. This assumes that you have installed the vulkan driver packages for your video card - which is beyond the scope of this gist. I set it up with its own wine prefix, so it wasn't affecting any others. Documented here so other people can give it a try - you will need to remember to specify the path to where you downloaded the installer:
env WINEPREFIX="$HOME/wine-doodly" WINEARCH=win32 winetricks dotnet48 dxvk corefonts mf nuget
env WINEPREFIX="$HOME/wine-doodly" WINEARCH=win32 winetricks renderer=vulkan
env WINEPREFIX="$HOME/wine-doodly" WINEARCH=win32 wine <path_to_installer>/DoodlySetup2.7.1_32bit.exe
Then to actually run, remember to replace with your actual username:
env WINEPREFIX="$HOME/wine-doodly" WINEARCH=win32 wine "$HOME/wine-doodly/drive_c/users/<username>/AppData/Local/Doodly/Doodly.exe"
The 'dotnet48' package will also install 'dotnet40' - that's fine, no manual actions needed. There are couple of additional packages installed in my wine-doodly prefix that I believe also got installed automatically due to other packages, but I'll list them here just in case they turn out to need to be manually installed:
env WINEPREFIX="$HOME/wine-doodly" WINEARCH=win32 winetricks d3dcompiler_43 d3dx9
I did find that the 'corefonts' package was essential - the login form fields would not function at all without it. Not sure exactly which font it needed, but installing the Windows default set (which is what corefonts is) fixed the login form.
Winetricks can be downloaded from github - I would highly recommend getting the version from Git instead of anything packaged in your linux distribution, because urls to the packages to download keep changing resulting in the linux distribution's version often failing to install packages because the url its using is out of date. Installing wine from your linux distribution should be fine.