Actually hyper-threading makes a very significant difference for dual core gaming, that's why the i3 is a relatively capable gaming CPU, but Pentiums are increasingly struggling:
http://www.tomshardware.com/reviews/gaming-cpu-review-overclock,3106-3.html
Also, HT is much more complicated than mrmez's example. If that example was true, there would be no benefit from HT which benchmarks clearly debunk.
Still, you're right that there's not many games that benefit from hyperthreading on quad core CPUs as 4 threads is usually enough.
However, when it comes to rendering, recording and streaming - all tasks that scale well with additional threads - HT starts to make a big difference.
Here's some benchmarks of a 4690K vs a 4770K -> the 4770K at stock clocks is almost identical to a 1231 (0.1Ghz higher base & boost clocks and Xeon has no onboard GPU, but otherwise they're identical):
http://www.anandtech.com/bench/product/1261?vs=836
You can see it's neck and neck until you run into certain multi-threaded benchmarks, where the i7's HT really pulls away.
If you can get an i5 to 4.4Ghz, which is pretty standard, then you'd be looking at about 25% faster, which will obviously beat the Xeon in poorly threaded tasks (like gaming) and will help close the gap or even catch the Xeon in SOME threaded tasks, while it won't be enough to close the gap for others (check out the 3D particle movement bechmark, for example, where the i7 holds a 75% advantage).
The thing to remember is that an i5 even non-overclocked, will rarely be the bottleneck in gaming, the GPU will be in almost all cases. If you're aiming for 144hz gaming, then OCing will probably make a difference, but at 60hz, it won't make any difference whatsoever, your GPU will be determining how many frames your PC can spit out per second. If that's the case and you're looking to stream/record/edit, then the Xeons start to make a lot of sense. They're more than capable of making sure the GPU is working as hard as it possibly can, and they offer a little more in your editing/rendering tasks.
If you're looking for a pure gaming computer, or your target is 144fps, then the OC'd i5 gets my vote. But if you're looking for a streaming/editing build with a 60fps target, then the Xeon is the better choice IMHO.