Out of curiosity, I hit up the Wikipedia entry for 'Climax locomotive' and came across this paragraph:
These featured a steam engine unit with two vertical cylinders mounted in the center of the locomotive. Class A Climaxes had a frame similar to a flatcar with wooden boxcar-like bodywork built up above it to protect the crew and fuel from the elements—this could be more or less covering between locomotive to locomotive. The front half of the locomotive, in front of the engine unit, contained the boiler. In smaller examples this may have been a vertical boiler, while in larger ones a tee boiler was employed. Class A Climaxes were small locomotives, generally under seventeen tons. Class A Climaxes, unlike Heisler and Shay locomotives, had two-speed gearboxes.
The description seems to match the model you acquired. Must be the earliest form of the Climax.
(I was still writing this when Don posted his reply)