Well, according to the documentation, “The System.Diagnostics namespace provides classes that allow you to interact with system processes, event logs, and performance counters.” So I guess by definition it fits. 🙂
But yes, it does seem a bit like an overloading of terms by putting it next to things a bit more obviously diagnostics-related (tracing, performance counters).
Still, I would say that the Process class is as much about monitoring running processes as it is about starting new ones. Monitoring is generally accepted as a diagnostic activity. Furthermore, it might be less intuitive to most programmers if the framework had split up functionality pertaining to the same item in separate namespaces. So I can see the logic of including it here.