I would interpret your graphic as demonstrating that intelligence is at least somewhat heritable. If your parents did well in school (at least got more of it) then the probability is that you will do so too.
Most cognitive ability tests measure analytical-type skills - good predictors of early college and graduate school outcomes. However, people with average analytical skills can make up for it with superior creativity, high discipline, persistence, and other traits. SAT and similar tests are probably the best single indicator of early college success, but they should not stand alone.
BTW, the fellow in my PhD program with the highest GRE scores (close to the 99th %ile) took the longest in our class to complete his doctorate. He is also arguably the least successful of our class. The people who were more timely and successful (immodestly including myself) had good analytical skills, but we were also more focused, customer oriented, and common sense-oriented.
I wouldn't interpret it that way at all. First, performing well on a standardized test isn't a reliable indicator of intelligence. All it means is that you did well on the test.
I think the more education one or both parents have, the more likely they will value education in their children and help them develop the skillset to do well in school or on these type of tests.
You do know, Bill Shockley got in trouble for saying as much (and more).