You have 2 problems I can see.
When you run it on your own machine, the account which the application is running as has permission to access the registry, however you are missing this permission on the other machine. When you run it on the other machine, can you try run it as Administrator or with escalated privileges ?
You don't have adequate exception handling in your codes Timer_Elapsed method to try/catch and handle the exception so it's crashing the entire application.
Also check if there's any anti-virus /security software running on the other machine which might be sandboxing the app or blocking access to the registry