“the way of the wilderness.” That is, the road to and through the wilderness toward the east.
“but the battle overtook them.” The Hebrew text is more literally, “but the battle stuck to them.” The Israelites were not letting the Benjamites escape the battle but were chasing them down. The NAB has that the battle “kept pace” with them.
“and those who were from the cities they destroyed in each city.” The Hebrew text can be read as “they destroyed in the midst of it.” The Hebrew text seems to be saying that the battle overtook the Benjamites who had come out of the city to fight, and then the Israelite army killed the rest of the Benjamites in the cities of Benjamin. E. Fox (The Shocken Bible) has, “whoever was from the town, they [the Israelites] brought him to ruin in its midst.” This explains how the tribe of Benjamin was reduced to only 600 men; the women and children had been killed. The Benjamite tribal allotment was small, and so there were not that many cities in Benjamin. Joshua 18:21-28 lists some 26.