I am having trouble getting my .NET application communicate with HIS 2010.  

With HIS 2013 I used a myapp.exe.config file to indicate the Remote Environment name, the local and remote LU names, and that TI object name.   

HIS 2010 seems to be much different.  It doesn't recognize my configuration file.  I tried creating a dynamic RE with the clientcontext, but that's failing too.  

What am I missing?

Have you taken a look at the HIS 2010 Transaction Integrator samples in the HIS 2010 SDK? The following is a link to the SDK documentation for the samples:

https://msdn.microsoft.com/en-us/library/gg164486(v=bts.70).aspx

You might also want to look at the following in the HIS 2010 Application Integration Programmer's Guide:

https://msdn.microsoft.com/en-us/library/gg164486(v=bts.70).aspx

Thanks...