As I said, this is bunk. If you pick a locomotive engine as a typical steam engine, you're going to arrive at highly inaccurate answers. Steam engines were specialty steam powered machines for moving massive tonnages across rails. These things had to weigh a lot and did weigh a lot. However, they were not the only example of steam engine available, and being on the upper range of weight, are poor references for airships in the same way that a 12-cylinder racing engine is a poor reference for a rubber boat.
A better reference for airships would be steam cars. These far lighter steam system drove motorcars in the early automotive days. If you remove the vehicle chassis, the steam hardware consisted of a boiler and pistons, likely weighing only 200-300 pounds, and a gasoline tank. Gasoline was used over coal because its energy density was far higher. Shoveling coal into a car was a really bad idea and nobody did it.
So, if you could create a miniaturized steam system based on similar historic car models, then why didn't they do that back in the day?
Because it's a pretty bad idea once you think about it. In the competition between the internal combustion engine and the steam engine, the internal combustion engine won hands down.
At first, it seems like the steam engine should win. These things are simple. You have a boiler or a steam generator, steam piping, and cylinders. That's it. Mechanically, the system was astonishingly simple. If it broke, you patched the tubing or you cleared something. In comparison, an internal combustion engine consisted of far more parts, many of which moved about.
The first issue consists of water. Gasoline engines don't need it except for their radiators, while steam engines are thirsty for water. Without a recirculator, a steam engine will exhaust its water very quickly. If you are in the air and you need water, you need to descend to get water, which is hard to do in the middle of the Atlantic or far away from civilization. Even with a recirculator, you would either need a daily water stop or you would need to carry far more water, and water weighs a lot.
The second issue consists of heat. Gasoline engines run hot and use radiators to dump the heat. The higher you go, the colder the air gets, which helps the internal combustion engine dump excess heat. In comparison, the efficiency of a steam engine depends on its ability to conserve heat. The more heat that an engine loses, the more fuel that it takes to keep going. Cold works directly against your engine. Even worse is freezing. If a steam engine must be shut down, the water inside the pistons will freeze if it's cold enough, and once they're frozen, getting them unfrozen is a difficult chore. A steam engine can't be restarted as long as there is any water remaining in the cylinders (you can't compress water), especially if that water's frozen.
The third issue is repair. Any engine that goes bad needs to be repaired in the air. Overall, gasoline engines were easier to repair and could run with misfiring cylinders. Steam engines tended to be more difficult to repair, as they had so few moving parts, and they either worked or they didn't. In this case, resilience beat simplicity.
If you didn't need an internal combustion engine, you could turn it off. Starting them back up was very straight forward. In comparison, starting up a steam engine is demonstrably more complicated. In the case of a boiler, you were better off maintaining its temperature, which cost you fuel. If you shut down the boiler, you had to reboil the water before the engine could work again. Presumably an airship would use a steam generator, which boils far smaller amounts of water very quickly. Even so, quickly is slower than starting a comparable internal combustion engine.
In short, steam engines were a pain in ass to run while airborne. (Truthfully, they were a pain in the ass on the ground, too.) Note that internal combustion engines of the day were a pain in the ass, too, just less so than steam engines.