Ping and RTT are two different things.
Ping sends an ICMP8 packet with random data. Usually the data is so small you get your optimal ping. You can get your common usage ping by sending one with a full packet of 1492 bytes. Normally, the pings you use are either 32, 64, or 128 bytes while real transfers use 1500-protocol (16+) bytes.
RTT on the other hand is the time between a TCP request of a given packet (or confirmation of packets arriving) in the stream and the packet actually arriving to you. Unlike ping where you get either a packet back, or a loss, the RTT actually measures the loss or the scrambled packets. Also, unlike ping, TCP doesn't ping/pong for every packet in an incoming data transfer, you get a lot of receiving packets and sometimes you send one, so the RTT is actually estimated.
As for games, if your game is using UDP, you can trust a regular ping to show somewhat correctly your reaction time to the game. If the game is using TCP, ping with at least 1000-1200+ bytes to get a timing that's somewhat near to your real ping in game. Note that not every game breaks the TCP packets in smaller chunks to send-as-they-come, most rely on the regular protocol, so they will fill up a packet before sending and that can increase your in game ping by a few milliseconds as well.