Remote Desktop Session's Machine ID for SQL Server Query
This information is not exposed to SQL Server. All SQL Server sees is the hostname of the machine they actually connected from (e.g. the RDP host).

Since they are connected using Windows Authentication, can you not infer from their login name who they are and what machine they are probably connecting from? You can find this information here:

SELECT session_id, login_name
  FROM sys.dm_exec_sessions;


You may be able to go out externally to Active Directory and somehow determine what machine(s) that user is currently logged into, or perhaps get their connection information from the Windows host, I'm not too sure, but you're going well beyond the built-in capabilities of SQL Server at that point, and I have no idea how you would then correlate that information with a specific session_id.

Another alternative would be to - instead of using RDP (assuming you are doing so because the server is in a different domain) - let the user connect via their local SSMS. Here is a way to do that across domains:

https://stackoverflow.com/questions/9671904/connect-to-sql-via-windows-authentification-over-vpn/9672170#9672170

In this case, the sys.dm_exec_sessions.host_name and sys.dm_exec_connections.client_net_address should be very meaningful.