Mythic Beast Shape says that I can cast spells as though I had Natural Spell.
This does actually have an effect, doesn't it? Last I checked, Natural Spell only worked for Wild Shape, and not for other polymorph effects.
Since you're asking, technically Natural Spell only mentions being able to cast spells while using wild shape (since only characters with wild shape are able to select the feat).
Considering the text in mythic beast shape is presumably intended to mean something, the intention is clearly that you can cast spells while using that option (perhaps the author thought of the feat's description "You can cast spells even while in a form that cannot normally cast spells" as opposed to the feat's actual rules text).
The mythic spell could have said something like "you can act as if you were a druid using wild shape with the Natural Spell feat", but I think that would be unnecessarily long (and probably lead to more confusion rather than less). Anyway, I don't think you'll find many GMs who'll say this doesn't work :)