Rav Moshe Feinstein ztz"l:
On the subject that a mitzvah that is binding upon each of us to review the Parsha each week twice in the original text and once in translation – and our rabbis, even the Rishonim, added that we should combine to learn also the Peirsuh Rashi on each portion – is very neglected, even by many Frum Jews.
It is simple and clear that no person is exempted from any mitzvah under rabbinic law based on the claim that he’s involved in Torah study. Similarly, no one is exempted from this mitzvah.
This is so even according to the opinion in Tosfos (Kiddushin 31a, s.v. lo tzricha, in the name of Rabbeinu Tam) that learning the Babylonian Talmud also fulfills the obligation to study Chumash because of the verses that are included among it. It is also true according to the Rambam (Hilchos Talmud Torah 1:12), that after one already knows the written Torah very well, he is no longer obligated according to the Rambam to study the written Torah at any time – and he certainly no longer needs to divide his study time into thirds. In any event, one is still obligated even according to the Rambam to dedicate some study time to the written Torah.
This being the case, it is clear that reviewing Shnayim Mikra v’Echad Targum is certainly included in one’s fundamental obligation of Torah study each week, for it was this learning that the Sages singled out for each week. It is certainly obligatory and one cannot exempt this study by learning something else from the Torah, neither written nor oral, other than this extra mitzvah that the Sages required.
Consequently, there is no exemption from this, even for those to whom Torah is their occupation like Rashbi and his colleagues. This is specifically true of our generation, in which no one can claim to be so expert in the Chumash.