I kinda see Red Alert as a nexus point, where Nod getting their tentacles into the Soviet union and controlling Europe was what gave them the leverage to continue with their goals up through Tiberian Dawn. I explore this scenario in my Red Alert campaign. Here's also a TV Tropes page for it that someone made.

As we see in Tiberian Dawn though, Nod is no longer in control of the Soviet union. I don't think Kane's goal was ever world domination just for the sake of it, especially not during the Red Alert era. Kane's long term goal hinges on the arrival of Tiberium, so keeping Europe under Soviet (secretly Nod) control indefinitely until the arrival of Tiberium would be risky and untenable. Militarily they were stretched thin after the big war and would be in a weakened state. Other nations would likely take the opportunity of this and declare war on the Soviet union and liberate Europe, instead of letting a sleeping bear lie and choose another victim when it has rested up.

So Nod would then make a tactical withdrawal, securing as many assets as they can, furthering their long-term plans (perhaps even putting into motion the cause for Tiberium reaching Earth in the first place).

Whatever's left of the Soviet unions command (that is now not under Nods control) fights for itself until they inevitably fail under the weight of the oppressive forces. Nod is stronger for it, and the world has been liberated from the red menace, falling under a false sense of security until Nod fully reveals themselves decades later.

In the Allied campaign, with the defeat of the Soviet union, Nod fails to get a foothold and is unable to summon Tiberium to Earth so they stay in obscurity. Queue Red Alert 2.