I'm running Ubuntu 9.04 with the latest updates. When it gets to the part where it is going to install the .NET framework, it briefly shows the .Net install screen then goes back to the previous screen. The .Net install screen looks very wierd. I will attach a screenshot so you can see it. Here is what Wine has to say about things:
$ wine ./InstallEufloriaDemo.exe
fixme:reg:GetNativeSystemInfo (0x33fea0) using GetSystemInfo()
fixme:advapi:CheckTokenMembership ((nil) 0x184dd0 0x33fe1c) stub!
fixme:advapi:CheckTokenMembership ((nil) 0x1817b8 0x33fce4) stub!
fixme:wininet:InternetSetOptionW Option INTERNET_OPTION_CONNECTED_STATE: STUB
I'm going to try installing .net on my own, then running the installer. I'll let you know what happens.