One of the features in TCP which can make TCP “slow” is that TCP is sometimes intentionally slow. For example, TCP uses a startup algorithm called “slow start” and other congestion-control techniques to avoid congestive collapse, i.e. your network blowing itself up and becoming useless. TCP uses rate-limiting algorithms to intentionally avoid swamping networks to make them useless, and if your game naively blasts out traffic as fast as possible, that's exactly what it will do if a lot of people play it.