Games don't care about bandwidth much. Unlikely almost every other kind of application games need very consistent latency between the packets. The game is calculating the delay between the different chunks of data it sends you to keep the user location in the client and server in sync.
When these delays vary this prediction does not work well and you get what a gamer user sees as lag.
The first thing to try is to use a ethernet cable to test. Wifi unlike most other forms of connection does error correction on damaged data, and there is a lot more damaged data on wifi than on other media. This error correction takes time and affects the delays between packets. This is fundamental design conflict
between games and...