It's going to fit. It's going to fit just like all the other reversible Type "A" USB plugs which have been around for years fit and have always fit.
The 'tongue' of the Type "A" plug is central in the middle of the plug, a little of its thickness one side, a little the other. The mating piece of the socket is and always has been just a little away from center allowing the plug to contact it. The only differences in this plug, the really only difference, is instead of the area behind the tongue on the plug one side being full of plastic, it's empty and the tongue has connections both sides.
If you look at the two pictures of the two plugs on the front page, allow a little leeway for the fact that they have been held at two slightly different angles, just imagine trimming away most (80%) of the plastic at the top of the 'old' plug to leave a hole.. you now have the new plug. That plastic doesn't do very much, adds a little bit of mechanical grip, makes the plug go in one way. The reason it's there at all in the original design is that making one set of contacts is cheaper than making two sets of contacts, one on either side of the tongue on the plug and the USB group was concerned to make sure USB plugs were cheap to manufacture. If you only have contacts on one side, the plug MUST go in one way up, hence the blanking plastic to ensure that happens.
I'm fairly surprised at the number replies castigating Apple for coming up with a plug which won't fit a normal Type "A" socket, number one because it's very clearly absolutely going to fit it and two because they just aren't that stupid.
If I am wrong and it actually does fit without shoving the electrode piece inside the port to the side, that's great. I actually hope that is the case. I even just watched a video that shows how it might, in fact, fit (though no explanation of how was given, just visual proof that it does fit).
All that said, I just don't see how it is possible, but hey, I have been wrong before and will likely be wrong again.