No it does not build Storm count. You copy the spell's effect of returning a non-land permanent but it does not put another Chain of Vapor on the stack.
This is not correct.
It's true that the storm count won't be increased, but putting another Chain of Vapor on the stack is exactly what the "copy this spell" part of the effect does. Storm counts the number of spells PLAYED, though. The original Chain of Vapor was played, the copies are simply put on the stack, not played, so Storm won't count them.