Yes, the seating shown on the right-hand side of that drawing is indeed a sort of "viewing gallery" for the ship's bowling alley. BTW, there was a bowling alley mentioned in an episode of TOS. In "The Naked Time," after he gets infected with that virus that strips its victims of their personal inhibitions, Ensign (or is he a Lieutenant?) O'Reilly takes control of Main Engineering and serenades the whole crew with an off-key rendition of the song "I'll Take You Home Again, Kathleen." In between verses of the song, O'Reilly at one point announces that there is to be a dance held in the ship's bowling alley. This, I think, is where Franz Joseph got the idea to include the bowling alley in his blueprints. So I think one can consider the existence of a bowling alley on Kirk's Enterprise as canon, since it was mentioned in an episode of the series.