Mono is a cross-platform implementation for Microsoft's .NET. However, since .NET is more complete and not all of its libraries can be implemented in Mono (legal issues), not all .NET-compiled applications will just work in Linux (or Mac) native Mono, so you have to run Mono through Wine to get these working. This may or may not still succeed. Try installing Mono through Winetricks. If that doesn't work, clean the wineprefix and try winetricks dotnet20 or similar. (I'm not sure what version of .NET the application requires, but older versions of .NET work better with Wine, so it is worth a shot.)
