That doesn't give re-distribution rights automatically. There's a topic dedicated to how to legally obtain games/ROMs, you may post there - respecting the forum rules - links to games you think are freeware/demo:
Why not set up a file server on the pi3 and have the piZero read from that directory for the roms and game saves. That way it will all be stored on the pi3 for OTG fun. You can have the pi3 host its one access point from the on board wifi and have the piZero connect to it. You can also have the piZero temp download the rom and save the game locally and once the game closes you can have it automatically sync the game saves using something like rsync.
Hope that wasn't too confusing but that all works! :)