That's an interesting observation you made! One reason for this could be due to the differences between glass and plastic when it comes to transferring heat.

Plastic is a much better insulating material than glass is. This means that plastic transfer less heat from the inside of the cup to the outside (it insulates the liquid inside the cup much better), as well as the other way around (it also transfers less heat from the outside to the inside, if there is a cold liquid in the cup).

You might have noticed this when you take the cups out of the dishwasher, the glass ones are still pretty warm/hot, whereas the plastic ones are not as warm. This is also the reason why coffee or other hot liquids are often served in styrofoam cups. Styrofoam is a specific type of plastic that insulates particularly well (although it wouldn't be such a good idea to put it in the dishwasher ... but that's another story).

So what does this have to do with the dishwasher? Well, after the dishes are cleaned, there is a drying step, in which hot air is used to dry the dishes. Since the glass dishes transfer heat better, they also get warmer themselves, whereas the plastic dishes don't get quite as warm (they are better insulators). Since the air in the dishwasher at that point is probably very humid (a lot of water was just used for washing the dishes), some of that humidity in the air will condensate (condensation is when water in the air turns into liquid on a colder surface). It will tend to do that on the coldest material that is in the dishwasher, which is going to be the plastic. That is probably why your plastic dishes turn out to be wet when you open the dishwasher.

Other reasons could be that the surface of your plastic dishes is not very even, so that small "puddles" of water can form on them, or at least are more likely to form than they are on flat glass surfaces.