The Page Layout can only be applied in a Publishing Page library page, not just any document library. If the Publishing Feature is enabled on the Site Collection and in the Sub Site, then there will be a Pages Library in the sub site. Page layouts can be selected in (and created and published to) this library only, not in any other document libraries.
Page Layouts can not be applied to just any document or wiki library, even if the Publishing Feature is enabled. The Publishing Feature creates a special library for publishing pages and one for publishing images (used in those publishing pages). In order to consume the benefits of the Publishing Feature, you'll need to use that specific publishing library.