As someone who's studied The Art Of War intensively, and to whom "defeat means friendship" (as long as the opposition does feel thoroughly defeated) is a matter of course,

Do you remember the other parts too? The parts that don't feel so warm and fuzzy? Or other effective military strategies? Defeat rather seldom means friendship when it comes to pre-established enemies, whether in The Art of War or outside of it. The generals discussed in The Art of War commanded their soldiers to kill other soldiers (and their leaders) and conquer strategic resources. The Art of War gives instructions on how to do so more effectively, with more compliance from soldiers and, where possible, in such a way that the enemy does not fight back significantly.

I find that incentivizing unforgiveness and wanton destruction (I mean, seriously, they even had to kill the cattle? How is that in any way practical or rational?) is not only aesthetically dissonant, but wasteful and silly as hell. Going out of one's way to ensure some don't get a proper ritual, or otherwise kicking the defeated while they are down, also strikes me as disgusting, wasteful, and, frankly, cartoonishly over the top.

Yes, God is silly as well as a dick (and non-existent). But looking at the strategy from the perspective of instrumental rationality interest rather than from the perspective of indignant atheism the cattle-killing silliness is not especially relevant. Most people agree that it is better to keep the cattle than kill them. What is more interesting is just when it is instrumentally rational to apply force (be that political, economic or physical) against those that are assisting a particularly troublesome enemy.

The details matter a lot of course. There are cases where it obvious that is instrumentally rational to kill those who are assisting the enemy while there are cases where that would be outright self destructive. On one side of the line there is the sole provider of particularly advanced weaponry to the enemy, who does not trade with you and who has no significant social alliances and on the other side there is an welfare charity who provides medical assistance indiscriminately worldwide, is loved by all and protected by an alliance of powerful nations. In between things are less simple.