A mathematician's confusion regarding parametric $t$ tests for gene expression data
I understand this in the following way:

For each probe you have two sets of measurements, one for ER+ and one for ER-. What you do is a T-test (to my understanding is that the "parametric" just emphasizes that T-test is a parametric test) on these two sets, testing if their mean is significantly different (they refer to this as "separated"). You repeat this test for all 7650 probes, and you get a set of 7650 p-values. You then do some multiple testing correction, such as a Bonferroni correction (I haven't checked in the paper if they did it, but they obviously should). Finally, they find that 606 of the p-values are significant (for some choice of threshold), suggesting that they can "separate" ER+ from ER-.

As a computational biologist I would advise you to look specifically at bioinformatics papers if you are looking into developing new methods, since the analysis in "pure biology" papers can often be lacking and would not give you a good perspective of state-of-the-art analysis methods. Specifically for the question of separating groups from gene expression you should look into the field of Machine Learning, as it had been widely applied to this problem.