I remember from last Daf Yomi cycle that there is a central argument whether Ochel Nefesh not for Yom Tov itself is a Torah Issur or a Rabbinic Issur. The Gemara in Shabbos about burning Terumah Temeah on Yom Tov states that there is an Aseh of burning Terumah against the Aseh of Shvittah on Yom Tov as well as a Lo Taaseh of burning something which is not necessary for that day. This sounds pretty explicit that such an act is a Torah Issur
You are referring to Rashi in Beitzah (12a), whom Tosfos (last Tosfos on the Amud there) infers is understanding that a Melachah normally permitted for the needs of Yom Tov performed not for the needs of Yom Tov is only forbidden mid'Rabanan, to which Tosfos argues.
However, even if this is Rashi's intention, there they are discussing doing a Melachah for no Yom Tov need whatsoever. But for the sake of G-d ("l'Tzorech Gavoha"), such as burning Kodshim, or doing Melachah for the day after Yom Tov, it is certainly forbidden mid'Oraisa from the Derashah, "Lachem -- v'lo le'Gavoha," as the Gemara in Beitzah (20a) teaches.