What Gretsch acoustic guitar has the whammy bar?

That would be the Gretsch Rancher G5034TFT, which is indeed fitted with a genuine licensed Bigsby tremolo! It is very unusual to see such a feature on an acoustic guitar. However, we can report that it functions perfectly well and is actually rather interesting to both play and hear. If that were not unusual enough, this guitar is also fitted with a Gretsch FideliTron pickup. This is exactly the same type of pickup found on many of their electric guitars.

Is the Rancher acoustic a new model or a reissue?

The Gretsch rancher guitars are a bit of both, really. They are indeed based heavily on the Ranchers of the 1950s. They include unique features such as the triangular soundhole and sweeping pickguard shape. These Ranchers have modern updates, too. Examples of this are the Fishman pickups and a revised shape that includes a Venetian-style cutaway.