I just read a good paper on this!

While breaking up groups could be viewed as genocidal for the groups involved, this was rarely the case since the cultures of steppe groups were so similar and survivors easily assimilated to their conquerors... All in all, it was a question of new loyalties. Only a very few were singled out as unredeemed enemies and even some of those were welcomed when they surrendered... Similarly, if sedentary groups resisted too much, refused to submit or, worst of all, revolted again after submitting, they ran the risk not only of continuing to be considered outsiders, but of becoming hereditary enemies.

This is the large majority of the answer.

One should heavily distinguish the modern notion of genocide, which is the destruction of an ethnic group, often with considerations of race, and Mongol policy. The Mongols left notoriously little evidence of their passing because they weren't supplanting anyone's culture. If they destroyed your ethnic group it was because they wanted to destroy you, not because of some inherent notion of cultural superiority.

As for no groups having grievances toward the Mongols, Russian historiography for easily a century blamed the "Mongol/Tatar yoke" for all the ways that Russia was not a thriving Westernized utopia. Additionally, the Ming, while owing a great deal to Yuan organization and accomplishment, were often not kind in remembering their predecessors. The raze of Baghdad was also a powerful symbol in that region, however, Baghdad was already in the shadow of Cairo, and thus was not as potent a symbol as it might have been.

According to wiki, the Mongol expansion resulted in 30-60M deaths. But which groups were annihilated?

Many of these deaths are more from suffering caused by the destruction of farm lands and simular things.

But which groups were annihilated?

No complet croupe was annihilated. The mongol did a job Xi Xia but the where not annihilated. The mongol destroyed your military, and will to resist, the had no concept of hunting down every single person of groupe X to destroy that culture.

It's surprising that there are no groups today with historical grievances towards the mongols.

There are. The ruissans have a long history with steppe people and where in constent war with them. There are still Muslims who hate the mongol, just go to youtube and watch the non historical mongol hate videos that some people put out.

The podcaster Dan Carlin tells a story, where he wrote a paper about mongol military and his chinese professor got angry because he did not spend enought time on the suffer of the civilians. So there is still some mongol hate in china, but I can not say how much.