“A mention of the miraculous wars was inserted into the prayers, but it seems that the Sages were concerned mainly with remembering the miracle of the oil.”
I think the premise of the vort is wrong. It’s not a mention, the tefilah just talks about the war and a passing reference about the oil. The Chachamim seemed to incorporate BOTH miracles, the oil in our actions (with a little reference to the war Maoz Tzur) and the war with our tefilos (with a brief mention of oil at the end). I don’t think the war was downplayed at all in our Chanukah observance.