Out of the box, rdlc reports will not run on computers that do not have SQL Server installed on them. In order to get them to run, you'll need to install
Right click on the project and choose properties. Click on Publish, then Prerequisites as shown below. Then check Microsoft Report Viewer 2012 Runtime and Microsoft System CLR Types for SQL Server 2012 (x64)
In the next step we're going to install these two manually because for most of our needs here that better suits our purposes. We write lots of small applications for a limited user set. A bigger scope will require that you build a deployment project and include these two in your deployment project. This article will not cover that.

You need to get these two components onto the client machine somehow. Generally, we prefer to build a folder and drop these into it and have the network admin just do the installs manually. As mentioned about, a bigger scope would require a deployment project.
So... we'll list the downloads below for the different versions.
CLR Types
Microsoft® System CLR Types for Microsoft® SQL Server® 2014
This is a little bit harder than it needs to be. Click Download and you'll get a popup. Scroll down and locate ENU\x64\SQLSysClrTypes.msi. Click on that and then Next.
Microsoft® System CLR Types for Microsoft® SQL Server® 2012
Careful. This page operates differently than the above. Click on Install Instructions. Scroll down to Microsoft® System CLR Types for Microsoft® SQL Server® 2012 then click on the link.
Report Viewer Runtime
Microsoft Report Viewer 2015 Runtime
Microsoft Report Viewer 2012 Runtime