And how is the chip supposed to get a signal without an antenna?? Everything has an antenna, it might be embedded into the casing like say a cellphone, but it has an antenna.
On a laptop the antenna is behind the screen only being blocked by a thin piece of plastic; putting antennas inside the grounded metal box of a desktop case would result in very little signal getting through.
Not sure why having 2-3 antenna cables coming out the back with the rest of your cables just "ruins the entire build"; I personally am worried about performance first. Sorry to blunt here but you are running a budget FM2 setup, your not rolling the Ferrari of computers here, more like the Nissan Sentra.
Here is 3 simple options for you:
If you want performance and no antenna: get the powerline adapter I have suggested twice now
If you want less performance for cheaper: get a wifi card with an antenna
If you want cheap and no antenna: get a small $5-10 usb wifi adapter and enjoy your 1-5mbps speed and choppy gameplay.