Even then, there are different classes of star ships. So Warped9's thinking of a mix of classes makes more sense than a singular class of ships on that chart.
Well, a single class of ships in the sense that all of these are starships (or Star Ships, or whatever). Multiple classes of starships there, some older than Kirk's, some newer.
The neat thing is, the list of names Jein was working from can easily be seen as a list of TOS starships from various classes
. It is, after all, a list of names to be used in TOS scripts, and it would stand to reason that TOS adventures would feature multiple starship classes rather than just one, especially when the ship in question would not be seen on screen.