To be sure, there's no explicit
mention of the Vulcans having warp-driven ships in 1957. We see two ships that lack identifiable warp nacelles or warp rings in 1957, and neither of them is seen at warp, or said to have moved at warp speeds. Quite possibly both ships might have reached Earth at sublight speeds, given the longevity of their crews.
All we learn is that one of the ships that didn't demonstrate warp propulsion had a "warp field engineer" aboard. Might be somebody who operated the ship's unseen warp engines. Might be somebody who operated the ship's ansible instead, though, because that's what the dialogue of the episode indicated: T'Mir asked this guy whether he could build a subspace transceiver for the castaways. Perhaps Vulcans knew that the space warp might be used for propulsion one day, but hadn't mastered that aspect of the technology yet?