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Your son as a gamer is complaining about the lag/latency (time taken to send or recieve information between him and the internet as well as back again). Latency is inherent with wireless connections and there is not that much that can be done to improve it past a certain point. Wireless communication cannot achieve the same speed of signal back-and-forth as wired and this is not likely to change anytime soon.
Cables are indeed 'messy' when laid across the floor, but it is very easy to run a cable under the edge of the carpet or under the house. There are 'super flat' cables available that make it easy to run under a living room rug as well (http://www.maplin.co.uk/p/cat-5e-flat-network-cable-20m-n87jx).
Basically, wireless internet and online games do not get along very well.