If by “I don’t think so,” you mean that you don’t think the Nova Vulgata is the official Latin Bible for the Roman Church, then you might want to check the Vatican’s website.
The Nova Vulgata is a corrected version of St. Jerome’s Vulgate. The scholars, commissioned by Pope St. Paul VI, corrected St. Jerome’s text using the critical editions of the original language (Greek and Hebrew) texts.
My guess as to the reasons so few of the Douay are in print - for your average Roman Catholic, most prefer more modern English that is more immediately graspable. For your average Eastern Catholic, our liturgical and Biblical texts and traditions do not have Latin is their linguistic foundation, so why would we bother with a text that is a translation of the Latin? So it comes down to simple economics. Although there is a demand for the Douay, it’s not a great demand all things considered.