See Shulhan Aruh Ha'Rav, Laws of Torah Study ch. 2, in Kuntres Aharon 1, that Rambam wrote Mishneh Torah as a practical Torah-law guide, and his opinion is that from learning his Mishneh Torah one could know the final Torah Laws without the reasons; see there. In the Shulhan Aruh Ha'Rav, loc. cit., it explains the statement by the Sages that "a (Jewish) person should divide his time for Torah study into thirds (i.e. three parts): Written Torah (the Hebrew Bible), "Mishnah," and "Gemara." There it explains that "Mishnah" as a general term includes any part of the Oral Torah that is recorded for the sake of basic knowledge. This includes those texts that present the opinions of established Torah Sages on Torah Laws in brief, without their explanations, like Mishneh Torah, Tur and Shulhan Aruh.
However, those sources that explain the reasons for the Torah Laws, such as Rosh and Beit Yosef, and those texts that explain the details of the Shulhan Aruh, are considered to be within the part of Torah that is called "Gemara" as a general term (which includes the Talmud, Midrash and Zohar).
According to this categorization, we can explain that anything that is within the part of Torah that is "Mishnah" is permitted for a pious Gentile to learn, because he is not delving into Torah; rather, he is just learning a text that teaches about Torah Law without its depth and reasons, as can be found in specific classic works, including Rambam's Mishneh Torah, Rabbi Yosef Karo's Shulhan Aruh, and certainly the Kitzur ("Abridged") Shulhan Aruh by Rabbi Shlomo Ganzfried, and likewise the Tractates of Mishnah itself by Rabbi Yehudah the Prince, without its subsequent explanations.
However, the explanations of the Mishnah, such as those of Rabbi Ovadiah Bartenurah, are considered part of "Gemara," as is explained in Likutei Sihot vol. 36, p. 17, because they explain the reasons and depth of the Mishnah.
But the Talmud itself, and the books of those codifiers who write in depth about the reasoning of the Torah Laws, like the Shulhan Aruh Ha'Rav, the Aruh Hashulhan, and the Mishnah Berurah, are definitely forbidden for Gentiles to learn, because this is called "delving into Torah."
This categorization is defined in responsa Mahaneh Hayim vol. 1, ch. 7. (the Divine Code by Rabbi Moshe Weiner, Ask Noah International, 2011, p 88).