Or maybe they didn't fight over ideas at all but resources and power.

So if you have an idea, and I have an idea, and I beat you to death, my idea has won?

Well yes, militarily defeating most proponents of an idea is a reasonably effective way of subduing that idea or ideology. For historical examples, the nazi ideology is probably a major example, with the idea becoming much less prominent and widespread after WW2, all the while it's obvious that it would be quite popular in much of the world if the war had turned out differently. The idea of divinely sanctioned monarchy is another big one which was generally accepted but then mostly lost out through applied violence. The USA Civil war might also be thought of as this kind of war of ideas.

I disagree. I would say we have phrases like "war of ideas" to differentiate between actual war. It would seem to me that literal war indicates a failure of a war of ideas. If what you say is true, then the only conclusion to draw is "might makes right". i.e. whoever has the biggest stick has the best ideas. That's something I'll have trouble accepting.