What does it mean for a person to fast Ramadan without performing the obligatory prayers?

Islam is a complete and integrated religion whose pillars reinforce one another. It is not befitting for a Muslim who fears Allah and is mindful of Him to observe some pillars while neglecting others. Those who fast but do not pray uphold one pillar of Islam but undermine another. They are like those who believe in part of the Quran while rejecting other parts, those whom Allah has threatened with the severest punishment on the Day of Resurrection.

And Allah the Almighty knows best.