Are you sure that doesn't have a iptables rule to blocking connections when exceeds the max amount of connections? For work with TCP outbound sockets of network and other network options you can use sysctl command.
You will need set the "fs.file-max" kernel propety via sysctl and change your local port range traffic.
fs.file-max = 360000
net.ipv4.ip_local_port_range = 1024 65000
Change these values to what you need, all kernel configs are located in etc/sysctl.conf.
Be careful with the time request of new connections, because you can lost the response if you don't change the tcp keep alive option in kernel.
net.ipv4.tcp_keepalive_time = 60
net.ipv4.tcp_keepalive_probes = 3
net.ipv4.tcp_keepalive_intvl = 90
Change these values according the latency of your host network in comparison to their clients (players).
If you have problems or bugs, ask for support in CentOS Community.
Good Luck!
Protimus's post in How can i set CentOS to support over 1024 concurrent connection? was marked as the answer