IMO, "Unable to complete version check" means, that launcher cant read current game version from local files (cleaned as result of error?) like in this post about PC version solution:
http://forum.square-enix.com/ffxiv/t...=1#post2964048

When file with version is empty, game not started (because cant does version check before). On PS4 we cant editing files then ... only solution (if SE dont change something) is install from scratch.