That's right.
It's what's written on the bridge dedication plaque, though I've never seen anyone take it literally as the class designation of the Enterprise before. But technically, the only reference in TOS canon to the Enterprise as a Constitution-class ship is in a barely (if at all) legible schematic that Scotty studied on a screen in one episode. It was one of those unofficial facts that fans took for granted from the reference sources but wasn't strictly canonical, until TNG referred to Kirk's Enterprise by that class name in "The Naked Now." (The bridge simulator in TWOK referred to it as Enterprise class, though that could've applied specifically to the refit. But Scotty's blueprints in TUC referred to the refit as Constitution class.) Although the Star Trek Concordance called the E a Constellation-class ship by mistake, and so a lot of other sources repeated its error.
For some reason involving trademarks or something, Pocket's style guide insists that we write "the Starship Namehere" (or whatever) instead of "the starship Namehere," even though the latter is clearly correct. These days they even do it with words like "battleship" or "warship" when they precede the ship name. (For this reason, I try to avoid having any of my characters actually say "the starship Namehere" under any circumstances.) So maybe some copyeditor did a global search-and-replace from "starship" to "Starship" and it affected Greg's "starship-class" sentence unintentionally.
that someone on Memory Beta listed them under alien races!
