Kail Tescar authored a number of online Star Trek comics featuring the original series cast. This 2003 effort, "To Dance With the Devil", features an opening scene in the Enterprise's bowling alley which appears to be inspired by the artwork cited above.
http://www.startrekanimated.com/tas_comic04_cover.html
Wow, how cool is that! Love his comics.
The bowling alley in "To Dance With the Devil" was indeed inspired by the image from "The Secret of Vulcan's Fury"! We try to feature interesting parts of the ship, when we can. We're talking about the swimming pool for the upcoming issue. Thanks for the kind words about TDWTD, that comic is actually being featured on our Facebook page right now.