I think the point is that the clock on the moon runs faster from the point of view of an observer on Earth due to time dilation. I can't claim to understand it, but clocks "run slower" the deeper they are in a gravity well. To an observer colocated with the clock, it ticks accurately.

This isn't a new problem, though. GPS satellites have atomic clocks, and they drift 7uS or so per day due to time dilation.