I'm sorry, my previous post didn't really provide an answer. Allow me to clarify. Rule 201.5 applies here.
201.5. If an ability of an object uses a phrase such as “this [something]” to identify an object, where
[something] is a characteristic, it is referring to that particular object, even if it isn’t the appropriate
characteristic at the time.
Even if the enchanted permanent is not an artifact, the "enchanted artifact" still refers to it because it's the object enchanted by Steal Artifact
. You apply the continuous effects in the following order.
1) Steal Artifact
gives you control of the Forest
2) Natural Emergence
gives the land the creature type.
3) Liquimetal Coating
(and later Silverskin Armor
) gives the land the artifact type.
After all of these effects are applied, state-based effects are checked to see whether everything is attached to a legal object. Steal Artifact sees that it's attached to an artifact, so it's happy. Silverskin Armor likewise sees that it's attached to a creature, so it's happy. The end result is that you will maintain control of the Forest. Even after the ability of Liquimetal Coating wears off, Silverskin Armor will allow the Forest to maintain the artifact type.
The important thing to keep in mind here is that, even though they apply in the same layer, Silverskin Armor's effect isn't actually dependent on Natural Emergence because Equipment always apply their effects to the equipped permanent. Normally, if that permanent isn't a creature, the Equipment falls off shortly after, but Natural Emergence makes the Forest a creature in time for Silverskin Armor to see it.