It really depends on a lot of factors. 2-3 sqft of room per bird is more for chickens. Its been my understanding that quail can be adequately housed in enclosures that provide at ABSOLUTE minimum 8inches per bird (This generally is for raising to 8 weeks before butchering or if you have a small flock that gets along VERY well) Minimum i provide my birds is usually about 1sqft.
I personally see no problem with the pictured enclosure. It looks quite comfortable for quail. However, when I used enclosures that small, I would always give them 4-6 hours outside in an open bottomed quail-tractor. I'd say if you're looking to keep them permanently in an enclosure that size; Something a bit bigger would be better. If they all get along well, and you don't have any bullies, that could be okay. I would flip that box over and cut a door so they have somewhere to run and hide if they need. And as mentioned, a small dish for a dust bath would make a big difference for them. I always found if you don't give them sand to bathe in, they'll just do it in the food and make a big mess. (and poop in it! Eww!) lol