That's not really accurate.
All DNS servers and your client on your computer will cache resolved domain names for a set amount of time (called TTL - time to live). When your computer attempts to communicate with a remote host (such as a game server) it will first check whether that record is cached and whether it's still current (i.e., the TTL hasn't expired). If so, it simply uses the cached IP address and does NOT contact your DNS server at all.
So even if you had a very high latency DNS server, it would only affect the first communication with a host, and then sporadic communication attempts in future once the TTL expired (anywhere from a few seconds, to an hour usually).
On top of that, if you understand how DNS actually works, it involves multiple requests to multiple servers, only one of which you actually control.
So even with your own DNS server, you're only in control of the latency for a tiny fraction of the overall time it takes a DNS server to return a record. For example, if I want to go to www.google.com.au my DNS server...
1) goes to the top tier DNS servers to find out who owns ".au"
2) then to the ".au" servers to find out who owns ".com.au",
3) then to the ".com.au" servers to find out who owns "google.com.au"
4) then to "google.com.au" servers to find out the authoritative IP address for "www.google.com.au"
Unless my server on the local network is utterly terrible, all the latency will come from communicating with all those other DNS servers.
In other words, even on the sporadic occasions when the cached records expire and need to be refreshed, unless your server is configured incorrectly, or there's some other issue going on, it's just not going to make any real difference to gaming latency.