In a way it was similar to how classical music contests are judged. No one could claim that they can measure the performance, so they rely on the subjective and imperfect judgments of the humans who are considered experts in music. One judge might be consistently high-scoring, another might be consistently low-scoring, and they might look at the different aspects (technicality, musicality, etc.). They just try to capture their ranking (voting) distribution.
In a way, the old system was more like voting. Even if the judge can't formally explain why s/he thinks skater A has better skating skills than B, the system would capture their preference. (And of course, this comes with all sort of biases – sequential bias, national bias, etc). But an important distinction is that in this system there is no proxy variable to optimize for.
In the IJS it's very clear what to optimize for. So everyone is doing it. Also, one of the major changes, of course, was eliminating compulsory figures from competitions. Modern skaters don't even know they existed as a thing. Nowadays, everyone knows that you win a figure skating competition not by having Patrick Chan level skating, but by rotating your body in the air quickly – that is what gives points. So in modern clubs all over the world people start learning jumps in the first half of a year of practice. Which, ironically, leads to the lower probability of them actually mastering the jumps, because you still need insanely good edge control for take-offs and landings.