We’re not speaking about chochmas yavanis – that’s something that the gemara said you can learn “when it’s neither day nor night” because it has no purpose. “Shaar chochmos” refers to math, science, astronomy, etc..
The shach on that rema says explicitly that we’re referring to math and science.
As for the shach’s grouping of kabalah in his list of shaar chochmos; i think – and this is just a theory – that he’s referring to people who aren’t mekubalim, and who read zohar because it’s interesting. Many people who “learn kabalah” really just read about ideas that they don’t understand. For torah she’baal peh, you’re not mekayam the mitzvah unless you’re understanding what you’re learning (unlike chumash). For the non-mekubal, the shach holds that you’re not engaging in limud hatorah on the level of sod; you’re just prattling away, so it’s no different than sichas chulin or chochmos.