Unlike normal public schools, where you need to apply and usually be accepted based-on merit, these prestigious high schools, will only accept people based on this one test. Therefore, the idea of this test is that it is "equal" because your grades and ranking and middle school and zipcode all don't matter when being accepted into these schools. The one sole factor is what you score on the SHSAT.
When 8th graders (or a few 9th graders, who want to transfer to these schools) take this test, they rank the 8 specialized high schools in order of which one they would like to attend the most to the least. Then, when people's tests are scored from 200-800, and the test administers will go from the highest scoring student and give them a seat at their top school if availble. If the student's top choice school is already filled then, the administers will try to put them into the student's 2nd choice if available, and if not keep going down the list of rankings. Eventually, all seats will be filled up in all schools, and after the students who got a lower score will not get a seat at any of the specialized high school.