In the following turn's combat phase, the pursuers will still count as charging. This might result in both sides having charging units in the same fight, in which case the charging units on both sides will get the normal charging bonuses conferred by charging (eg causing impact hits, benefiting from lance charge etc.
Let's parse this here; first sentence describes how (in a particular situation - overrun / pursuit) pursuers will count as charging.
Second sentence, before the comma, says this (overrun / pursuit) might (can possibly) result in a particular situation. That situation is; both sides having charging units in the same fight.
Second sentence, after the comma, speaks of what happens "in which [this] case". The case is
not pursuit - because only sometimes (might) does this result in both sides charging. The case is "both sides charging".
Ergo; counter-charge does NOT negate impact hits - based on this ruling. Both the unit charging the regimental unit (Orcs, say) and the detachment (Empire) are charging in the same combat. Both gain the advantage of impact hits etc.
It is a fair and reasonable assumption that "charging" is done to a specific unit - one cannot just be "charging", one is charging SOMETHING. So, one only gets one's benefits
vs that unit(s). This is something where a RAW ruling is harder to find - but I think it's pretty obvious what is intended.
And it is certainly the case a RAW ruling using pg 58 is in accord with "counter-charge does not negate charge bonuses".