You seem to have two routers, which is undesirable, but not the problem here. You already have a ping spike to the first hop outside of your own network (3), so I'm guessing you're suffering from bufferbloat due to a congested connection.
The DSLReports speedtest (http://www.dslreports.com/speedtest) will tell you how much (looks like it will be at least 300ms).
There are two possible solutions:
1. Replace your two routers with 1 good one that can do SQM-QoS. This way you'll never have to worry about what others (or your own PC) decides to do while gaming.
2. Stop whatever is causing your connection to get congested. This might lead to fun discussions with family members or house mates to make them stop downloading, youtubing, netflix when you game.