Having tried out "obsolete's strategy" for myself in a few games, I have to say that it doesn't need to involve a bad military or even a Cavalry rush. In fact, it's very evident to see what ABigCivFan means when he says that obsolete is needlessly shooting himself in the foot many times by refusing to lightbulb or cottage or even expand substantially in the first parts of the game.
Even when you're wonder spamming in the capital, it's easy at Noble or Prince to establish a solid empire supported primarily with your second or third cities. In fact, one of the best things about obsolete's build is that you can easily shift to building units and if you get the opening right, there's a comfortable space between ancient and medieval wonders to do some Maceman or Cata building, often a one turn apiece. The key thing is Industrious or Philosophy to boost the GP/Wonder feedback loop, and either Great Prophets or Great Engineers.
obsolete doesn't like GSs all that much because they don't strongly support the feedback loop and GAs are even worse because they don't even have the food the GM gets or the science the GS gets. Personally, I think that obsolete would have done better in one of his games to have sent the GM for a trade mission, rather than settle him.
If you're more selective about your wonders, you can even attack a neighbor with a Swordsman/Cata stack late in the Ancient period, though this probably won't work on higher settings or against Aggressive AI.