>wars between the city and the village
I like this simplification. Or essentialization perhaps.
>It was a class war.
Lolno. No "class war" was ever fought in history.
>The Reds were led by city slicker intellectuals/factory intelligentsia
>the Whites were led by landlords.
Russia had a large mass of peasantry and a comparatively small group of workers (they were a lot, but if we compare their ratio to peasantry they were relatively small group). The civil war was essentially a war between your "factory intelligentsia" and "landlords", who fought for the power over the mass of peasantry by making the peasants kill each other ie. the average soldier on both sides was a peasant.
Btw the Soviet forced industrialization was also an effort to destroy peasantry as much as possible and make workers out of them, communists hate peasants, because they can be self-sufficient, but workers are dependent on the services the state provides. Same with cities. Urbanites can be choked by cutting basic services - stopping food, water, electricity, heating - therefor easier to keep in check. Funny consequence was the dacha system where workers had to do agricultural work on the weekend so they can maintain a bare minimum of living standards.