KU's rival is (was) Mizzou. K-State's rival was Nebraska. The in-state game, the "Governor's Cup", is something that nobody in Kansas cares about, unless K-State does not win it.
The KU/KSU rivalry only ever has the characteristics of rivalry on the days when KU pulls off a win against K-State in football, or when K-State somehow manages to beat KU in basketball.
This would be akin to calling the Vandy-Tennessee series a rivalry.