What is the non-ideal equivalent of mass action kinetics?
According to Catalytic reaction rates in thermodynamically non-ideal systems Journal of Molecular Catalysis A: Chemical 163 (2000) 189–204 (citing to kinetics textbooks) non-ideal kinetics needs to consider the activity of the transition state in addition to the activities of the reactants:

For $\ce{A + B -&gt;}$

rate $=\frac{k_BT}{h}K^{\ddagger}\frac{a_Aa_B}{\gamma_\ddagger}=k_0\frac{\gamma_A\gamma_B}{\gamma_\ddagger}C_AC_B $  

Where $K^{\ddagger}$ is the equilibrium constant for the formation of the transition state, $a$ is activity, $\gamma$ is activity coefficient, $C$ is concentration, $k_B$ is Blotzmann constant, $T$ is temperature, $h$ is Planck's constant and $k_0$ is the thermodynamically ideal rate constant. 

Another reference to look at for more info is The status of transition-state theory in non-ideal solutions and application of Kirkwood–Buff theory to the transition state J. Chem. Soc., Faraday Trans. 2, 1986,82, 1297-1303.