signal strength vs signal quality
They key reason wireless has issues is not the strength of the signal but the quality. In general the lower strength of the signal the poorer the quality is but it is not as simple as that. You can have poor quality at high signal strength if the interference from another device is also at high signal strength. Put the right cordless phone or baby monitor on top of your router an I promise you you will have 100% signal strength but a totally unusable wireless connection.
Now when you look at the so called speed reported by a router that is assuming that the data packet actually gets there. What they don't say is how many times the packet had to be retransmitted because it was damaged by interference. There is all kinds of overhead in retransmitting packets.
The key reason games see more issues is they send a large number of small data packets at a consistent rate. They are very dependent on the rate being consistent but retransmission of packets make the rate vary. In the voice over ip world this is called jitter but unlike a voice call where a person can tolerate a little noise many games are greatly effected by jitter.