you have the bot msg somewhere (channel is my guess) the players action and/or result.
change the way it posts the text from just msg to writing/playing a text

mIRC will queue the texts to be played thereby delaying the replys to the order in which they were received, one reply at a time.

you might have now something like:
on *:text:-action *:#channel: {
do stuff
msg #channel stuff
}

instead do it:

on *:text:-action *:#channel: {
; create or clear a text for that user
write -c $+($nick,.txt)
do stuff
write $+($nick,.txt) stuff
;play the text to channel
.play #channel $+($nick,.txt)
}