Now that the Theros Release Notes have been released, we have an answer. This is what the Release notes have to say:
* Monstrous isn’t an ability that a creature has. It’s just something true about that creature. If the creature stops being a creature or loses its abilities, it will continue to be monstrous.
So it's not an ability, it just something that's true about that creature. If you Clone a creature that's monstrous, the Clone will not be monstrous, so you'll be able to use the monstrosity ability of the Clone.
Nathan Long
DCI Level 2 Judge
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