It does have grass this is the muddy end down by the watering holes where the rhino like to roll - and it is a wet February by the look of it! Cant see how you can judge the size from this photo?
I can confirm this is a comparatively large paddock, and it doesn't seem, at least to my amateur eye, to be overcrowded.
This water hole is at the far end, and the muddy area extends quite a bit further than the photo shows (depending on the weather admittedly). There is a hillock in the centre of the paddock which I'm pretty sure is grassed and I've seen the zebras make good use of this galloping up and down.
Probably the best way to appreciate the size is to go to Google Earth ..... the zebra/rhino/giraffe/ostrich paddock is clear to see on the left hand side of the 1st view you come to (before zooming in). This is beneath the other large paddock for the elephants. If you zoom in you can see the individual animals and therefore appreciate more the space they share.