Gemara: “Even in private (the prohibition applies).” This refers to the decree of the Hasmonean court (Beit Dino shel Chashmonai). For when Rav Dimi came, he said: “The court of the Hasmoneans decreed that one who has relations with a Gentile woman is liable due to Nashga [the acronym for niddah, shifchah, goyah, and eshet ish].” When Ravin came, [he explained further]. This is the correct text (katzar l’omra). See also in Tractate Sanhedrin, Chapter “Hanisrafin” (Sanhedrin 82a) for further clarification

Tosafot, beginning with “משום נשג”ז וכו’”: Indeed, it is difficult [to reconcile this] because we say in the chapter Kol HaAsurin (Yevamot 49b) that Abaye said: “If a Kohen has relations with a Gentile woman, even if she is a married woman, he does not incur lashes.” And Rava said: “He does incur lashes.” This implies that, according to Rava, it is a Torah-level prohibition (mide’oraita), since lashes are administered for it. The explanation follows Rava, as we rule in accordance with his opinion over Abaye.