I made sure and I have all the same settings you posted. WMM is enabled in the router. I am using the latest drivers for the 7260. The OS is Windows 8.1 64 bit. Type of authentication is none (open) (my closest neighbour lives 300m away, so no one is going to steal my wifi :P). The PC is in the room next to the router, so it's less than 2 m away but with a wall between them (I always get 3-4 out of 4 bars).
I was also suspecting the issue might be the router. Yesterday I installed dd-wrt firmware on it and forced AC-only and VHT (80+80 MHz) on the 5GHz channel. I still got the same slow speeds and worse, no internet connection, so I reverted to the stock firmware. BTW, I have a laptop with Intel Ultimate N Wi-Fi Link 5300 and I get 200+ Mbps on 2.4 GHz and 180+ Mbps on 5GHz. I still think that I should get more speed because the theoretical limit of the 5300 is 450 Mbps and the computer is really close to the router. So I don't know if this is a router issue or a combination of both. What I am really sure is that I shouldn't be getting 87 Mpbs at most on the 5GHz for the 7260 adapter and 144 Mpbs at most for 2.4GHz.