> Nuclear missiles are normally hypersonic,

Ballistic missiles usually are, cruise missiles usually are not; both can be nuclear (or not).

> so it seems like the difference is that these are cruise missiles and not ballistic missiles?

The combination of nuclear, hypersonic, and cruise is what is significant, yes.

They are referring to hypersonic glide vehicles here. Whereas conventional warheads follow a ballistic trajectory that can be predicted while in transit, hypersonic glide vehicles (HGVs) can at least to a limited extent maneuver. HGVs also tend to fly on a lower trajectory than ballistic warheads, meaning they are more difficult to detect by radar. These two factors make HGVs good at getting past current anti-ballistic missile (ABM) systems like those the US has spent a lot of time and money developing.