I can verify everything works, and the previous post was completely correct with the steps that need to be followed (I'll repost them below). Sound also works in game. I also can verify gameplay seems to work great (I played about 4 hours as of this post). I did not need to run a setup, just ran the game directly.
First, .NET Framework, won't install under a 64-bit Wine. - so you need to create a 32-bit winecfg and install .net40 & XNA40 under Wine Arch 32.
WINEARCH=win32 WINEPREFIX=~/.wine32 winecfg
env WINEARCH=win32 WINEPREFIX=~/.wine32 winetricks dotnet40 xna40
Then change to the directory you downloaded 'Hacknet' to, and run:
WINEPREFIX=~/.wine32 wine setup_hacknet_220.127.116.11.exe
What does not
I experienced some weirdness with some display resolutions when in windowed mode. When in windowed mode, some things would not be clickable.
The game starts with fullscreen mode set, but it does not start in fullscreen. I found if you just change the resolution, but leave the fullscreen setting set, it will stay windowed and you can play that way just fine.
What was not tested