Michelasso on 10 June 2016
Sure the PS4 Neo will run all previous games. If a game won't it will be most likely because of a bug in the PS4 OS/Graphics API or drivers and it will be up to Sony to fix it. Unless a developer implemented some hacks in the code, which should be against the Sony policies. In that case the devs will have to patch it. Yes, it may happen, but one would imagine they will get the new development kits before the PS4 Neo launches.
It isn't much different from Windows (or OS X), actually it's much simpler. Only two platforms, same identical OS, with the main difference just being the much more capable GPU.
