1. Check out some benchmarks, friend.
2. That is mostly what I was saying. But it's a lot slower in productivity as well.
3. Xeon/iGPU isn't remotely relevant here. 1080p is a CPU bound resolution in a majority of cases(games). This is simply fact.
Passmark is not exactly a great benchmark, but I'll play...
The 8400 is still around 25% faster in your link. At 1080p, that can make a difference in 1080p gaming. That CPU would need to be well past 4.5 GHz to match the 8400 (which you can also lock all c/t to its turbo clock). Please look at some reputable benchmarks. What I'm sharing is all out there.
In the end though, if you have $150 to try and build a PC, what the heck CAN you do but buy generations old hardware? It is what it is... but throw a little budget at it, and the experience can be quite a bit better. I do understand what you are saying though.