it could mean rivals to sora. but i think it means to eachother. vexen lexeaus and zexion, close as they are, are still rivals in a way. yes they do work togethor in an organization togethor. but still there rivals. for example a quote from zexion.(the organization used to be the rope that binds us, and now it's full of kinks) he directs this comment at vexen. and vexen gets insulted, and you can instantly tell there's a rivarly between the two.
lexeaus appearently dosent join in this rivarly as much as zexion and vexen do, but still the three are like a trio, so it still counts. plus there probably rivals of science as well.
now, the rivalries between xigbar xaldin and demyx. huh absouletly just about no connection between them...yet.
this rivalry if there is going to be one will probably be more explaied in the final mix. becuase right now the only connection is the numbers 2,3, and 9. you may notice vexen lexeasus and zexion's number completly matched as 4,5,6 to signify the trio. so 2,3,9 would be the other rivals. becuase it coudn't be 1 because he's the superior he dosen't need rivals. number 7 is like the second in command, so he dosen't need rivals either, unless it's with xemnas in some way, and number 8 is a runaway renegade so it dosen't count.
so you have the next number up which is 9 demyx. making 2,3, and 9 a perfect fit.
now one last thing, if this was just a rivalry to sora. it should say enemies not rivals. enemy is actually an enemy, while a rival would be someone like riku, a friend, but still someone you compete against.
so i think with this im about 99% sure that this rivalry is between the organization themselves and not at sora.
well that's about it thanks for reading.