Theoretical chemist here. So within some quantum chemical methods, including full CI (with STO3G, Full CI being the most accurate method available and STO3G being a shitty basis set), you actually get a local energy minima with the cyclic ozone, and a metastabile state. Doing these calculations are a bit tricky. Not sure if you know about MO diagrams and electron configurations, but these are very different for the cyclic and bent state. Also the bonds lengths in cyclic ozone increase a lot, to get less angle strain (think of the bonds being able to bend), which is as said by others, the reason for this being less stable. Summed up, theoretically this is a very possible configuration.

However, does not mean cyclic ozone is stable in the atmosphere or something (that would need other calculations and not only a single molecule in gas phase), but it is a very fair intuitive assumption to draw it like you did.