Hsin Kang Theater 新港戲院 is located in the small town of Xingang, Chiayi, not far from the famous Fèngtiān Temple 奉天宮. Multiple sources agree it went out of business in 1988—a victim of shifting consumer preferences and demographic changes in small town Taiwan—but the actual age of the building is somewhat uncertain. This academic reference suggests it was founded in 1929, in the midst of the Japanese colonial era, but the theater was almost certainly renovated or completely rebuilt in the post-war period.
After many idle years the theater is now rented out for use by the big Mazu temple in town, the halfway point of the immense Dajia Mazu pilgrimage 大甲媽祖遶境進香活動 (also see my account here). There is some talk of turning the old theater into a traditional arts center or something but presently the interior is only used for storage, as can be seen in this television news report. With a horseshoe-shaped balcony level it reminds me of another post-war theater, Xinxing Theater in Xinpu, albeit with a recently renovated rooftop.
Finally, a note about naming conventions: usually I roll with standard pinyin but in cases like these where there’s an official Wade–Giles romanization out front I’ll use that instead. If you’re interested in more information about this theater you’ll find it mentioned here, here, here, and here, all in Chinese of course.