The picture is from an atmospheric train, so I'll assume you mean that instead of "atmospheric engine". This is doubly good because Zeiss Ikon already answered that alternative.
Yes, it could be built, the technology and materials needed were available to Hero of Alexandria centuries before. He probably could have made one if somebody had paid for it.
It would be quite ineffective. The idea in the 19th century was to use steam engines which were not available in your time frame. You could use wind or water power instead but that has serious restrictions that reduce value. Air pumps would also have been less efficient due to less precise manufacturing.
More importantly before industrialization the resources needed to build and maintain the railway would have been extremely costly and there would have been no demand for large scale transport to pay for that. You need industrialization first, railways second.
Temporary railway to transport material for a specific large scale project might work. Or a short vanity project. Think building Taj Mahal or the Pyramids, or giving the guest to Royal Palace really cool way to arrive. But usually in such cases human labor would be the easier solution. But with specific circumstances... Why not. Hero did build pneumatically opened temple doors. A king might want "a house moving on tracks" and be able to afford it.
Another option that might be available is a short railway inside an industrial complex. If you are planning to build up local technology in some way concentrating your manufacturing projects into one location makes sense. You might have wind or water mills then use pneumatics or hydraulics they produce to power machinery. And if you use pneumatics you can also build an atmospheric railway inside the complex and it might be worth it since you'd already have the materials and trained personnel right there and the complex would actually have a need to constantly transport stuff.
What was generally used was canals. Building canals is highly labor intensive but the materials and maintenance are in general affordable. This matches pre-industrial economics much better