You are correct that the sulfur on cysteine can either be protonated or deprotonated (there are no intermediate states), so it would seem like an equilibrium constant would not be useful for a single molecule. However, you must remember that chemical systems are dynamic and equilibrium is dynamic. What do I mean by that?
Let's say you are looking at a mole of cysteine molecules in water that has a pH of 8.33. Now, from the Henderson-Hasselbach equation, you know that when the pH = pKa, half of the cysteine molecules will be protonated and half will be deprotonated. If you take a snapshot of your mole of cysteine in water, you will see exactly that.
Now, let's zoom in on one of the protonated molecules (R-SH) and see what happens over time. This cysteine will float around in solution bumping against water molecules and occasionally, during one of these collisions with a water molecule (or perhaps an OH- ion) it's proton will fall off (attaching to the water molecule instead). The cysteine is now deprotonated (R-S-). It will then spend some time randomly bumping into water molecules until one of the water's protons falls onto it, protonating the thiol again. As you track this cysteine over time, you will see it randomly flipping back and forth between the protonated and deprotonated states. Now, if you look for a long enough time, what do you think the ratio will be between the time spent in the protonated state versus the time spent in the deprotonated state? The answer is 1:1... the equilibrium constant. So, the equilibrium constant does give you information for a single molecule. Instead of telling you about the relative concentrations of each form of the thiol, it tells you about the fraction of time that the thiol spends in each state.
This equivalence between the statistical behavior of a large number of particles at one particular instance and the statistical behavior of an individual over time is known as ergodicity, and it is a common and important property of many chemical systems. Can systems be non-ergodic? Sure, human gender is a common example. If you look at a large number of people, you will see roughly an equal number of men and women. If this system were ergodic, you would expect then that an individual would spend roughly half its life as a man and half its life as a woman. Clearly, this is not the case (for most individuals), meaning that human gender is does not display ergodicity.