Good chess players, though, exhibit some common traits which are shared with “smart people”: the ability to think in abstract terms, and a good memory.

Your success at chess is often based on how far in advance you can plan a game at any point on the board, greatly supplemented by your ability to remember entire games of famous matches. These skills are frequently exhibited by people considered smart. However, as you and OP point out, you have to play, practice, and memorize to get good; merely knowing the rules and being smart doesn’t get you there.