This sounds like the "games server" you are trying to connect to is set to use only the 2.4 GHz band, whereas your new WiFi unit in the computer is trying to use the 5 GHz band. The solution depends on what else is using WiFi where you are.
1. The simple solution is to re-configure your new WiFi adapter to use the 2.4 GHz band so it matches the configuration of the server WiFi system. Depending on how that is done, you may find it easy or not to change to 2.4 GHz when gaming, and 5 GHz at other times.
2. IF nobody else is using the 2.4 GHz WiFi system at the server, and IF you do NOT have any other WiFi devices trying to use that system, then you could re-configure the WiFi unit at the server to use the 5 GHz band instead. This might give you faster data transfer for gaming (not sure if that would make any difference for you, though). For many WiFi transceiver units, it can use only one band at a time, so changing to 5 GHz means that ALL devices in the area using that WiFi source would need to be configured to work on the 5 GHz band. Also note that, although 5 GHz is faster and has more channels available, often its range is shorter because of signal attenuation, so in some cases it may not work for you.