Do generic Void Rift skill nodes work for all Void Rifts?

For example, Erasing Strike has a skill node called Rifts of Destruction that says it increases the damage that Void Rifts deal, not specifying that it only applies to only Void Rifts created by Erasing Strike. Would that increase the damage of Void Rifts created by other abilities or passives?

No, skill nodes only ever affect their own skill (or things proc’d by it in this example) unless explicitly stated that it’s a global effect.