Well, if running is bad for qi or health, it should be perfectly obvious that fighting is worse.
I think it may be true that ancient Chinese soldiers did not use running as part of their training in any systematized way. That's possible because their battlefield strategies and tactics didn't require their soldiers to run, and ordinary citizens didn't run for work or fun. Ok.
However, that's entirely different from the claim that running is bad for health, which is a complete exaggeration. Walking is bad for health if it's done excess. Anything is bad for health done when done excessively. Doing qi gong 16 hours per day wouldn't be good for one either.
Anyway, another way to describe over-training is "when the rate of injury exceeds the rate of recovery." If it applies to muscles (and muscular energy), it also applies to "qi." That is, if qi can be used up, it can be replenished. The problem would be in using it up faster than it can be restored. The same with breathing and oxygen. Call it moderation, but the point is that it applies to everything, even aerobic and anaerobic exercise.