The move itself is small (depending if the Chess-software is sending only the move or additional data (e.g. a FEN of the position)) this is sginificantly less than 150 bytes.
Depending on how moves are transfered one moves takes about 500 to 800 bytes. You should check the size of the package sent by your ping: If you ping 184.108.40.206. you should get something like
64 bytes from 220.127.116.11: icmp_seq=0 ttl=60 time=12.638 ms
64 bytes from 18.104.22.168: icmp_seq=1 ttl=60 time=12.814 ms
64 bytes from 22.214.171.124: icmp_seq=2 ttl=60 time=15.309 ms
The lag might change during daytime or even seconds depending on the load or setup of your provider.
More important seems to me that the ping to 126.96.36.199 lags with you for 245ms - this is way too much (I e.g. get 12ms). So probably your provider is too slow.