The large house across the street was definitely not the mosque because before it became the Startup hub, it was called 金華官邸, which is the house for the Premier. Just until last year William Lai was still living in it.
The address of that house is 金華街142號, instead of 麗水街17巷2號。
The site sits the on boarder of Nishikichō (錦町), Fukuzumichō (福住町) and Shōwachō (昭和町) when the Japanese built it.
Back in 1948, when the mosque was at 麗水街17巷, the house was occupied by Peng Mengqi (彭孟緝) who was one of the main perpetrators of the 228 incident and subsequent White Terror. He is also known as the Butcher of Kaohsiong. Peng moved to that fancy house because he got promoted for his actions during the 228 incident a year prior.