"Now, would it be correct to interpret this is as a probabilistic result?"
Yes. There is a mathematical equivalence between 0.5 probability and 50% chance.
However, strictly speaking, one cannot assign a probability on the basis of statistical information, for the reason that you point out in your last sentence. So what statisticians provide is an estimated probability to allow for the uncertainty that attaches to empirical premises. They allow for variability in the results by assigning a "confidence interval". So one would assign 50% chance to people with Z gene and a confidence interval which indicates how variable that figure is likely to be.
This is all very fine if one is talking about groups of people. It is less obvious what it means if one tries to apply it to a single case. Indeed some people think it is meaningless to apply a probability to a single case.
However Bayes' theory of probability does exactly that. You can look up the details Wikipedia -- Bayesian probability. Intuitively, I feel that the 50% version of probability is less appropriate here, in a single case. But few people agree with me and would insist that probability=50% and probability=0.5 mean exactly the same.
So your question becomes "what does it mean to say that there is a fifty percent chance, if you take a new random person with Z gene to have a disease Y?"
This could be the basis of a bet, but not of a prediction. But predictions, yes or no, are not everything. Probability is not useless. If the probability of rain tomorrow is 50% and you're going out, it makes sense to take an umbrella. It makes less sense if the probability of rain is 5%. Probability combined with expected utility justifies taking out insurance on your life, your house, or your car. Probability justifies locking the door when you leave home. and so on.
I haven't specified the meaning in the usual sense, but I have given some examples of the uses of probability. Whether those are the same thing or not would have to be argued elsewhere.