The "Water pipe" analogy works extremely well for the internet. It doesn't matter how many taps you hook up to a water pipe, but how much water each tap tries to consume. Same thing with networks.
As long as you don't consume more than about 90% of your bandwidth, you shouldn't notice any issues.
eg. If you have a 30mbit line and Netflix is pulling down 5mbit and your video game is doing 1mbit, you still have 24mbit free.
90% is a good rule of thumb for networks. As long as you don't consume over 90%, your games should work just fine and you shouldn't have buffering issues for your streams.