Before discussing why or why not something should be an ikkar/principle, we first need to know what the principles are in the first place. I answer that here: What are Rambam's "עיקרים"?
Discussion of this question should begin with noting that the Gemara itself asks this very question in the very beginning of Perek Cheilek (Sanhedrin 90a):
וכל כך למה? תנא, הוא כפר בתחיית המתים - לפיכך לא יהיה לו חלק בתחיית המתים, שכל מדותיו של הקב"ה מדה כנגד מדה
Why should his punishment be so severe? He denied Resurrection, therefore he should have no share in the Resurrection, for all the manners of God are measure for measure
This Gemara, however, poses a severe difficulty for the Rambam, because the Mishna (that this Gemara is referring to when it asks why the denier of Resurrection is punished so severely) is discussing having a portion in Olam Haba, the afterlife, which according to the Rambam is very different than Resurrection! The Ran (chiddushim there) asks this on the Rambam, and answers that there are actually two opinions in the Gemara as to whether Olam Haba and Resurrection are equal, and this represents an alternative view than the one to which the Rambam ascribes. This is answer is also a bit difficult though, because it implies that the Mishna itself follows an opinion other than the Rambam's, despite the fact that the Rambam paskens like this mishna.
Another explanation for the Rambam is given by the Sefer HaIkkarim (4:31), that the Gemara freely refers to two different things as 'Olam Haba', both the Resurrection as well as the afterlife. Despite the fact that they are two different things, they can both accurately be described as worlds that are 'to come'. However, this would leave the question of the Gemara either unanswered (because the 'Olam haba' of the answer isn't the same one as the question), or it would mean that the Rambam understood the Gemara and Mishna to be referring to the Resurrection, in which case he has no basis for saying (as he does in Hil. Teshuva 3:6) that the denier of Resurrection has no share in the afterlife.
An alternative solution (I thought this myself for a while, and discovered today that I'm not the only one who does) is that the Rambam does believe that Resurrection is some form of divine reward, even if it isn't the ultimate reward. Someone who denies the Resurrection is symbolic of the fact that he denies God's ability (or willingness) to provide a person with reward, and therefore he deserves no reward in the ultimate sense: the afterlife. Admittedly, this too is rather weak, both because it doesn't sound like that in the Gemara, and because it's perfectly plausible that someone believe that God wouldn't perform a miracle as radical as resurrection of the dead, but He does provide a non-miraculous from of reward: spiritual afterlife.
The Rambam himself addressed this issue in his Letter on Resurrection, which was written mainly as a response to the claim that the Rambam didn't believe in physical resurrection of the body (because after all, as the question notes, why should he?). Inter alia, he gives an explanation for the importance of the principle of Resurrection:
שזאת ההכחשה מביאה להכחשת הנפלאות והכחשת המופת, כפירה בעיקר ויציאה מן הדת
Denial of this (Resurrection) brings one to deny the miracles and signs, denial of the principle [of Judaism] and removal from religion.
It seems that the importance of the Resurrection for the Rambam has nothing to do with reward, but because the act of resurrection is crucial to the acceptance of miracles. The only reason to deny resurrection, the Rambam is saying, is because he doesn't believe in miracles, which is a belief that is absolutely required for religion. Such an answer does have its difficulties (as theoretically a person could believe that God performs miracles but not such a radical overhaul of natural laws, or that there's no need for such a miracle, etc.) but that seems to me to be the most straightforward reading of the Rambam. I unfortunately have no good explanation (or any explanation at all, really) as to how he fits this ide with the Gemara in Sanhedirin quoted above.