Fabrice-
I am wondering if you noticed or tried this step in the build instructions, which are found about halfway down in the link you referenced:
"1. In the Solution Explorer, right-click the SpatialQueryREST.Manager project, and click Build. If your project fails to build and you are running ArcGIS 10.0 Service Pack 1, you might need to add one more string argument, serviceTypeName, to LoadConfigurator in your Configurator.cs code file. For example, the C# implementation of the line of code defining LoadConfigurator looks like the following: public string LoadConfigurator(ESRI.ArcGIS.Server.IServerContext serverContext, . . ., string servicesEndPoint, string serviceName, string serviceTypeName)."
This applies to any service pack with 10.0.
Best wishes,
Sterling