No Official Answer
Unearthed Arcana is playtest material, so there are bound to be mistakes. The page you linked to, The Faithful, was subsequently updated in Wizard Revised. The next article in the series, A Trio of Subclasses has a link where they were collecting feedback on Wizard Revised, but it is expired.
I didn't see anything in the revised version that answers your question. Getting an official answer to your question will have to wait until it actually becomes part of an officially published product, or they release another revision and ask for feedback again.
Considering that the latest version explicitly states using your Wizard Spell Save DC where other saves are required, I would also substitute Intelligence for Wisdom and Wizard level for Cleric level in any powers granted through the subclass. Despite a theological background, the character is still a Wizard. In fact, one of the later abilities mentions coming earlier than clerics get it because of the character's method of studying to learn it.