Yes, there must be a full installation of ArcGIS on the client machine.
Developers should consider installing the ArcObjects .NET Developer Kit located under "Getting Started/The .NET FrameWork" at the below link:
This installs the ESRI assemblies; otherwise the ESRI assemblies must be included in the deployment package.
Developers should note that method calls will fail if the client's ArcGIS product does not have a license for that specific functionality. For example, ArcGIS-ArcView does not have the ability to create coverages so calling IArcInfoWorkSpace::CreateCoverage will result in an error.
Refer to the ArcObjects Developer Kit > Technical Documents > Licensing Issues for more details.