Only an idiot will buy that product. Horrible specs for the money. You can literally buy a netgear R7000, or an Asus RT-AC68U (far better specs with 3 stream WiFi AC1900, with gigabit Ethernet).
For about 55% less money, you can get a Netgear EX6200 (AC1200 range extender) (5 gigabit Ethernet ports).
PS, for the PC gaming stuff, if the range extended is function as a true range extender, then it will not introduce its own NAT, thus from the perspective of the main router, it will not be able to tell that you are connecting from behind the range extender. Local multiplayer only becomes hindered if you end up with a double NAT. Most range extenders will not do this.