I honestly think if you did something open air like that, you'd need to attach a plastic shower curtain on three of the sides. Day geckos and such and recommended to be kept in tanks or combo screen and glass. However there is nothing wrong with open air enclosures as long as you maintain high humidity with them. They need less mistings than chameleons but have generally higher humidity requirements, though still need to dry out. It is recommended that their regular humidity for a general basis on day geckos stays at 65 to 70 percent and no lower, spiking sometimes to 80. This means very short mistings, just enough to get things wet. So that the moisture can maintain humidity and they can drink, but it doesn't stay stagnant. That's why it's usually recommended for them to go in live planted enclosures. However with rehabilitation cases, I never do that. Just so that the gecko is easy to observe and the droppings are easy to find. He should be fine in a ten gallon enclosure at least until he is healthier. Then a single individual should be fine in a 20-25 gallon enclosure.
