It's the "SS Woden", ( http://memory-alpha.org/wiki/Woden ) . Though I wouldn't use the 'canon' registries from remastered for much, since Okuda deliberately chose them to screw over existing fandom or older material.
Other notes, while the Antares and similar ships are old, keep in mind that their configurations in both TOS and TAS have to be a post-2245 uprating due to their nacelles and engines. If they appear prior to that, they need a completely different nacelle/engine scheme (maybe Baton Rogue style). Of course, there's nothing preventing the ships actually being younger than the Enterprise, though, and we can just assume that Charlie (who mentions the Anatares as being old) as just being an asshole to cover up and excuse his mass murder.
"Thank god I'm only watching the game... controlling it!"