From the context it is clear that it has something to do with one player having bad H2H against another player. Could somebody give a clearer explanation when this word is used? Etymology of this phrase could also bit interesting. Has this originated from some common idiom in English?
A player that is easy to beat, an easy prey. If you beat a player too many times, he/she becomes your "pigeon".
informal a gullible person, especially someone swindled in gambling or the victim of a confidence trick.
This term has been commonly used as as a slang as far as the 20's in American English.