Actually at the bottom of page 2 of Maynard's preprint he states: "We emphasize that the above result does not incorporate any of the technology used by Zhang t

Actually at the bottom of page 2 of Maynard's preprint he states: "We emphasize that the above result does not incorporate any of the technology used by Zhang to establish the existence of bounded gaps between primes." So it seems like it is actually a coincidence, though they were both building off of the same previous work (GPY) so maybe it's not that surprising.