A parasitic interaction is when one species has a fitness increase from this interaction (benefit) while the other has a fitness decrease (cost). Note: you don't need to have physical contact to have an interaction. As soon as the presence of one specie influence the fitness of the other, it is enough to consider that there is an interaction.
In the case of Batesian mimicry, I think it is obvious to understand why the non-toxic species gain from this interaction. Let's imagine the toxic (model) species is blue. Predators learn to avoid blue species because they feel very sick right after eating it. In other words, the predators have a bad experience or even better we can say that the predator receives a punishment or a negative reinforcement (instrumental conditioning). In consequence the predator that got this negative reinforcement will probably avoid blue individuals in the future.
When a predator eats an individual from the mimic non-toxic species, he got a positive reinforcement. In consequence the predator learns that the prey tastes good and in consequence it is more likely to eat a blue prey next time it encounters one, which obviously has a negative impact on toxic model organism.
Now, I have two issues with this concept.
The interaction is not one-to-one and we can consider that the presence of a species that use Batesian mimicry influence the variance in fitness of the toxic species only if (actually you might argue differently by not assuming infinite population size) the distribution ranges are not completely overlapping or if there are some kind of population structure.
If the toxic species causes death to the predator, then the predators never get the opportunity to learn. But one can consider the same mechanisms at evolutionary timescale than at the time of the lifespan of the predators. It is also possible that the predators have higher cognitive abilities allowing them to gain insights concerning the toxicity of one species without having to taste it.
What if predators can tell the difference between the two prey species?
Your point, if I understand it, is that if the predators manage to sense (or to evolve sensing) the two prey species differently (in consequence the non-toxic species does not mimic the other prey species anymore), then the toxic species will not suffer anymore from the mimicry. So in other words, mimicry is a parasitic interaction but predators might evolve ways to sense the two species differently in which case there would have no mimicry anymore. Note: the predator is more likely to evolve good sensing abilities if it forages on few species only.
I think your issue is that you should not consider a species to be mimicry if the predator can tell the difference between the two prey species. It is not to the human eyes that the mimicry makes sense but only to those of the predators. So, batesian mimicry is a parasitic interaction and if the predators evolve so that they can sense the difference between the two species, then there is no more Batesian mimicry and there is no more parasitic interactions between the two prey species.
Why do you say that "physical contact" not necessary for two species to have a parasitic interaction?
The interactions between species are defined as follow:
The benefits and costs (harmed) are defined in terms of fitness. These definitions do not involve any physical interactions. And to the eyes of the evolutionist at least, that would not make much sense to add a notion of physical interaction into these definitions.
In the case of Batesian mimicry the ± effect is not always certain (while it is certain in common parasitic interactions)
The point is interesting. I think it just mean that the non-toxic organism is a facultative parasite (a species that can live with or without the parasitic interaction). Statistically speaking, if you have enough preys of each species and especially enough predators, then the consequence is certain.
Consider the common Ivy. It is a parasite of other plants but can also live on human-made walls in which case the negative effect on other plants is not always certain either. The difference between the Ivy and the non-toxic prey is that the fitness of the non-toxic prey depends on whether it parasites the other species while the Ivy is doing just fine on human-made walls.
You can think about the interactions between rabbits and wolves. They share a prey-predator interaction which is a special case of the parasitic interaction according to above diagram. In a particular environment the wolves might be absent and so predation does not occur, just like the non-toxic species might be absent species might be absent and so the parasitic interaction does not occur anymore.