Like ants, termites have an elaborate social structure in which a few

Without the by, (C) is open to another interpretation: maybe "tending, gathering, and building" are things that happen as a result of serving the colony -- those ants serve the colony, and in doing so, they are tending, gathering, and building. In other words, the tending, gathering, and building might be the result of the serving, not the mechanism by which they serve.

To make matters worse in (C), why is there a "by" before "battling" but not before "tending, gathering, and building"? This actually compounds the issue -- is there a "by" in front a "battling" only because "battling" is the only one that's a mechanism of the serving, while the others are results of the serving? The meaning is open to interpretation. (This is a great example of how flawed parallelism can affect the clarity of a sentence.)

In (E) we don't have that ambiguity. there is no question that "tending, gathering, and building" are things that those ants do to serve the colony. How do those ants serve the colony? By tending, gathering, and building.

I hope that helps!