Currently the WikibaseClient extension is only able to retrieve data from MediaWiki SQL database tables. So, the Wikibase client should have access to the Wikibase repository database and to use the WikibaseClient extension to build a Wikidata client you need an access to the Wikidata database. It have been done this way in order to have enough performances to serve Wikidata-Wikipedia connection (with millions of articles each pulling data from multiple items and a feature that refreshes the article when an item it relies on is updated).
I don't think that the Wikidata developpment team is going to work on having an API-based backend anytime soon for third party client. I believe it should be a great project to start one.
For now you could the linked wiki extension that allows to pull data from Wikidata using the SPARQL based Wikidata query service.
Comment on theorist answer:
for the client to be able to fetch data from Wikidata.
If you setup your own repo the client is going to fetch data from your repository, not from Wikidata.
doesn't the repo get populated with data from Wikidata? – theorist – 2017-12-03T10:08:05.647