Got it running on mono now.
Changes to http://www.runningcode.net/2015/01/30/request-compression/:
The http module has to be registered here as well:
<!-- Required for MONO -->
<system.web>
<httpHandlers>
<add path="*" type="ServiceStack.HttpHandlerFactory, ServiceStack" verb="*" />
</httpHandlers>
<httpModules>
<add name="GZipRequestDecompressingModule" type="YourNamespaceHttpModules.GZipRequestDecompressingModule, YourAssembly" />
</httpModules>
</system.web>
And, additionally, I had to remove the line request.Headers.Remove("Content-Encoding");
, because "HTTP Error 500: System.NotSupportedException - Collection is read-only."