Rashi explains that when the gemara tries to prove that R. Yossi Haglili holds of איסור כולל from the fact that when yom kippur falls on shabbos and he does melacha he has to bring a korban both for shabbos and for yom kippur. Even though YK and shabbos are entering at the same time, one can only be liable for both since if theoretically one would start before the other, each can be binding on top of the first. Rashi explains that even if shabbos would enter prior to YK, the prohibition of YK would be binding on top of shabbos as an איסור כולל. The fact that YK forbids not only doing melacha, but also eating and drinking makes it an איסור כולל to allow the prohibition of melacha to be binding on top of the prohibition against doing melacha on shabbos - מיגו דאיתסר באכילה משום יוה"כ איתסר ליה נמי מלאכה משום יוה"כ. The difficulty of this rashi is how can we say an איסור כולל from the issur to eat to the issur to do melacha, they are totally separate prohibitions. From rashi we learn a new approach in understanding the nature of the issur to eat and to do melacha on YK. Although in the counting of mitzvos they are completely independent, and would seemingly be two completely separate prohibitions that apply on the 10th of Tishrei, that is not how rashi is viewing it. Rather, the kedusha of YK results in two halachos, one is a prohibition of eating and the second is the prohibition of melacha. Both are outgrowths of the kedushas ha'yom and not independent prohibition that apply to the calendar date of 10th of Tishrei. It would now make sense that Rashi can consider YK in the general sense to be an איסור כולל from eating to melacha, since both are merely outgrowths of the kedusha of YK.
I would like to suggest that the Rambam would not agree with rashi. Rambam (Hil. Shevisas Asor 1:6) writes that the mitzvah d'oraysa to add to YK before and after is limited to YK (not shabbos and yom tov) and limited to the עינוי of YK, it doesn't extend m'doraysa to the issur melacha. The Minchas Chinuch clearly understands the Rambam this way. The Rambam would seem to hold that m'doraysa when one is me'kabel YK early, they are prohibited from eating but not prohibited from doing melacha. The fact that by accepting kedushas ha'yom one can be prohibited from eating but not from melacha implies that the they are not an outgrowth of the kedushas ha'yom, rather two independent halachos that apply on the 10th of Tishrei and could theoretically exist one without the other.