I would me more worried about other predators, like foxes. If cats are not an issue during the day, they usually won't be any more of a risk at night. Foxes will try to break in, especially after dark. The are very persistent when they know there is captive prey. It can also be stressful for the rabbits, which can cause them other health issues. So I would look at the overall security of the rabbit playhouse.
Looking at the photo, I would consider:
- bolting the wood frame onto the concrete slabs to prevent digging in
- cover the remaining gaps in the frame (ie atthe top) with decent thickness and small hole weldmesh.
- maybe double mesh the outer frame with thicker weldmesh, leaving the smaller hole stuff as it is.
- decent bolts and padlocks on any opening door or window - and use them. Bolts and hooks can be rattled open.
Cats, foxes, stoats & similar will all climb / jump in through any openings. Thin wire can also be chewed through or just forced at a weak point. Hence recommending to cover all the frame to make it predator proof. Bolting it down will stop it being forced from ground level. The slabs are really good as it stops anything tunneling through (either in or out). If the holes in the mesh are too big, paws & claws can reach through, and teeth can get a better purchase.
I have thought about doing something similar with a wendy house. It provides a good space for bunnies and good access for their people.