Both of these chrome postcards are from the late ’60s, when Doe River Gorge Playland was in business (check this link).  As you’ll read on that webpage, for about a year, it was Hillbilly World and it closed in 1971.  I’ve hiked the gorge twice, once from the Ministry side and once from the highway side.  I think the one on the left shows the Engine #1 at Pardee Point, the one on the right is just a general shot of the engine steaming along.
The technical details: On the left: the card is badly creased end to end.  Shame, that.
On the back: “Doe River Gorge, Highway 19-E, Hampton, Tennessee
A panoramic view of the Doe River as it winds through the Doe River Gorge.  This is just one of the many scenic views of natural beauty seen from “Little Whistler” as Engine Number 101 puffs through the 3 1/2 mile trip in the Gorge.”
Published by KING PRINTING 509-511 Shelby Street, Bristol, Tennessee 37620
(there’s a small logo on the back: KING ADVERTISING DESIGN – PHOTOGRAPHY – COLOR SEPARATION – LITHOGRAPHY BRISTOL, TENN U.S.A.)
It’s been scribbled on, apparently by a child.  Postally unused.

On the right: Card is in pretty good shape.
On the back: “Doe River Gorge Highway 19-E, Hampton, Tennessee
The “Little Whistler” puffs up the 2% grade road bed of scenic Doe river Gorge.  Steam engines have been pulling this grade for nearly one hundred years. A trip through Doe River gorge offers one of the most scenic natural beauty views in the southeastern United States.”
All rest is same as above.