Err, well, no.
Simply being "steam" does not make something steampunk. A steamship is not steampunk. A steam tractor is not steampunk. A steam hammer is not steampunk. If I was to write a story about a steam powered ferry that plied the waters of the Hudson in the 1790's, even that would not be steampunk as that really happened.
Likewise, air rifles are not steampunk. They were deployed in the Napoleonic wars. (Napoleon hated them, too.)
But, you say, the Ironmongers are in an otherwise fantasy world, but only they have advanced steam technology. That should make them steampunk, right? Again, that would be wrong. I focus their general technology on the years 1800-1815. There is nothing "punk" about what they do with that technology.
In my mind (and only in my mind), the primary adjective of steampunk is "fantastical". That is to say, some element of reality is ripped away to enable the story to exist. For example, inventing a steam-powered dirigible that can fly in space sounds steampunk. There's a whole host of wrongness there, but we won't worry about it. We'll just accept the fantastical and move on. There's nothing wrong with that. The second aspect of steampunk is speed of invention. The inventor in a steampunk novel will turn out a sophisticated machine in unreasonably short time, and then is an expert at working that device.
There is nothing fantastical about Ironmonger technology. If you saw it, you would be singularly unimpressed. It doesn't break any laws of physics. None. You could drop their tech into our world and it would just work. The only reason it seems fantastical at all is because nobody else has anything like it.
As for aesthetics, Ironmonger inventions have all the design charm of a German battleship. Let's just not go there.
So, in a sentence, just because you like steampunk doesn't make everything steampunk. There is a term for term, however, that better describes my Ironmongers: derivative. Another possible term is cultural (mis)appropriation.