Yes, White plays first. There are other cases of this in the Keian era c. 1650. They are marked "Shiro toku ban", that showing Black (Sanchi) was really the stronger player. Yasui II Sanchi was noted for his sense of protocol. He had been introduced as a young prodigy to the shogun Iemitsu, and the Yasui family was then also close to the separate court of the retired Emperor Go-Mizunoo and played games in famous places like the Kinkakuji in Kyoto. This game may have been played there. Imperial courtiers used the colours differently from everyone else so as to delude themselves they were toffs.
Sanchi briefly became Meijin-Godokoro by exploiting his contacts. His heir was Shibukawa Shunkai, the subject of a new film, though that mainly focuses on his role - even more valuable at court - as an astronomer.