It mostly depends on how you characterize the real God.
Is it interested in mortal affairs? Is it benign or malign? Does it care for free will? What are its thoughts about the "people's god"? Does its power rely on faith, or is it in fixed amounts?
From your question, you state that:
Now let's imagine that this world indeed had a REAL God that created it. This God who doesn't need any power from people, because he already is too powerful before the creation of the world.
I'm assuming here that the original god, since its responsible for the whole creation, is somewhat aware that people beliefs can materialize into paranormal entities. Being an entity of limitless power, he isn't interested in the whole procedure.
But then again, from your description of the facts, your original god must be quite the absent one. The people's god get following because it actually interferes with ordinary life - hence, we must assume that the real one does not.
Since the original one seemed uninterested from the start, there is a good chance it will remain so. Depending on how much powerful you make it, it may even be so out of reach than the other god isn't a threat to it.
Or maybe, the original god is following some grand scheme of things, limiting its intervention in subtler, less noticeable ways. For example, the original god may be willing to talk only to the purest of human being, on of the likes that is born every millenia. Or it may consider unethical to directly speak to mortals, not wanting to tamper their mind with his divine wisdom and omnipotency. In short, if the original god is following some sort of code of conduct, it isn't likely that it will break it without a good reason.
Now, a good reason could be that the people's god may be perceived as "absolute evil®", or its presence may be an offense to the original god. If this happens, you have to ask yourself how the power scaling works in your world.
Maybe the original one is very powerful, but only in some aspects (it can create the world) but lacking in others (it can't alter human minds).
Maybe the original one is omnipotent, but the people's god power escalates exponentially for every new believer. The original one may send packs of his angels (or other kinds of emissaries) to deal with the people's god, but this in turn could rally more believer to his side (let's remember that the people's god is the one answering prayers, after all).
So, you've got yourself quite a good deal of possibilities.