The word clearly does have a meaning. Merriam-Webster say it's this:
opposition to depriving a legally established state church of its statusI thought it was something like the movement against the separation of church and state, but maybe that's the same thing - I'm not at all clear about what that actually means. But the point is that the meaning arises directly as a sum of its parts: it's compositional. Well, this isn't strictly true: there is some idiomatic meaning to do with the church and the law as well. But the length of it comes from attaching affixes with strictly compositional meanings. When you have compositionality, you can theoretically create longer and longer words, up to the limit of your cognitive capacity. I could add a morpheme and create antidisestablishmentarianismation, for instance. Some long words in quite common use aren't in the dictionary simply because they're made by standard suffixation processes, and that suffix is in the dictionary so you can work out the meaning for yourself.
So antidisestablishmentariansim is a real word, in the sense that people recognise it and can understand its meaning and it's made with proper word-formation processes. But for M-W, it's not a word in common usage. They have only three quotations for this word which use the meaning they give above, and dictionaries rely on written uses of words. This is why they can seem slow: words only get in when they've achieved plenty of use in print materials.
They do have plenty of quotations of the word with reference to it being a long word, however. It is in the OED, and their quotations refer to this:
1984 T. Augarde Oxf. Guide Word Games xxvi. 216 The longest words that most people know are antidisestablishmentarianism..and supercalifragilisticexpialidocious.
Interestingly, M-W say at the end of their piece that it might be considered a viable entry 'simply because it's a well-known word'. The meaning is not well-known, however, so it would be an entry whose definition read something like 'famous long word', and the definition as a secondary bit of information. That would be quite cool and very meta.
Irrelevant postscript: There's a really stupid joke that goes like this: 'Antidisestablishmentarianism is a very long word. How do you spell it?' and the answer is, of course, 'I, T'. I sometimes try that out on my students and some of them groan but a lot of them simply don't understand the joke. Maybe it's the way I tell 'em.