You are right on. It's running, just at a lower state. If we had better measurements, my guess is that we would say it is "running."
No, you're not understanding, this has nothing to do with power states or whether or not the computer itself is running. Instead, the zeno effect is put to use where the photon isn't actually run through the program, but (for lack of a better description) only influenced by the program. We know that an unstable particle can never decay if it's being observed, but the observation does influence the particle and alters it. That's what's at work here.
I guess it depends on what the meaning of "running" is.