Due to neutral kaon mixing, the and are not eigenstates of strangeness. However, they are eigenstates of the weak force, which determines how they decay, so these are the particles with definite lifetime.
Furthermore, the linear combinations given in the table for the and are not exactly correct, since there is a small correction due to CP violation. See CP violation in kaons.
Note that these issues also exist in principle for other neutral flavored mesons; however, the weak eigenstates are considered separate particles only for kaons because of their dramatically different lifetimes.