When John Albert Victor Rushworth performed the marriage on 15 Aug 1914 he was described as 'Officiating Minister'. This term is used when a clergyman isn't attached to the parish where he is taking a service - in other words, whatever appointment he may have held, it wasn't at St Andrew's.
The Vicar of St Andrew's at that time was William de Lacy Evans. From looking at the register, in 1914 he performed no marriages between 25 July and 16 Sep, leading us to guess that he might have been ill or on holiday. A page that's already been referred to in this thread notes that he was appointed Vicar in 1882 - see
http://www.leedsindexers.co.uk/_Leeds.html#Trade_DirectoriesDigging further, we can find out a bit more about John Albert Victor Rushworth. There are some editions of Crockford's Clerical Directory at Ancestry, and he can be found in the one for 1932. If anyone wants to check, this is on p.1136 of the book, image no.1141 of the set.
This indicates that he was appointed Perpetual Curate of Stourton in 1921 (that is presumably the St Andrew's near Waddingtons' factory), but from 1914-21 he was Curate of St Simon's, Leeds. As the Leeds Indexers article notes, this was a parish created by taking a portion out of St Andrew's Cavendish Street (in 1869). So in August 1914 he helped out by taking a marriage in the next-door parish while the vicar was unavailable.
His later appointment to a different St Andrew's is therefore just a coincidence.