There are several points raised by your question and by some of the answers so far.
Powerline networks are available to run at different speeds typically from 200 Mbps to over 1 Gbps. This is the maximum speed that can be achieved but it depends on the quality of the house wiring and also on any obstacles in the signal path such as electricity meters, circuit breakers and surge suppressors. If there is a clear electrical path between Powerline adapters they generally work well. Also, unlike WiFi they can support full duplex signalling.
A Powerline network can have more than just two adapters on the network. Personally I have run networks with four adapters, but I believe the limit is around 8. Only one adapter needs to be connected to the router and the other adapters can serve different devices (PCs, games consoles etc). Each extra adapter has to paired on to the network to set up its connection and security.
There are also Powerline adapters that provide two or three Ethernet ports, which eliminates the need for any external way of feeding Ethernet to multiple devices.
Ethernet splitters allow a single wall port to carry two separate Ethernet connections to two devices. This works because the normal Ethernet UTP cable (such as Cat5 or Cat6) has four conductor pairs. For 10 Mbps and 100 Mbps Ethernet only two pairs are used. Splitters allow the other 2 pairs to be used for a separate connection.. For faster Ethernet connections, all 4 pairs are used so splitters are not suitable. Splitters have to be used in pairs with one at each end of a long cable. Typically the two splitter ports at one end will connect to two router ports, and the two splitter ports at the other end can connect to two devices (for example: a PC and a games console). Splitters are totally incompatible with Powerline networks.
If you only have one Ethernet connection available from the router, then using an Ethernet switch is the best way to connect multiple devices to the router. Hubs are functionally similar to switches, but only allow a single packet to pass at a time. Switches can allow multiple packets to flow providing they are travelling in opposite directions or between different devices.
Finally, for online gaming, WiFi is normally a poor choice. WiFi can pass only one packet at a time, and when it gets busy packets can be lost. Other devices on the network, and nearby rival networks and other electronic devices can make WiFi slow and can make ping (lag) times excessively long.
I hope this helps.