Normally you'd say something like "that's an unnecessarily elaborate word".

Except for verbose, none of the following are common, but I've marked the very rare:

• 
  rococo (adj) having elaborate ornamentation wiktionary (rare)


• 
  baroque (adj) very elaborate wiktionary
  


• 
  elegant variation describes using synonyms to avoid reusing a word wikipedia
  


• the lure of the abstract describes the use abstract words instead of concrete ones Plain Words (rare)


• 
  circumlocution (noun) is a speaking around the topic and being very indirect (rare)


• 
  pleonasm (noun) covers the case of using too many words wikipedia (academic, rare)


• 
  sesquipedalian (adj) is the use of long words instead of short, only ever seen humourously wiktionary (academic, rare)


• 
  logorrhea (noun, rare) is using too many words, also verbosity and prolix
  


• 
  high falutin' (adj) is a pejorative phrase for "over-educated": "You and your high-falutin' words, just trying to confuse us!" (US, very informal)

You can call this flowery language.

According to Cambridge:

flowery (adj.): disapproving

If a speech or writing style is flowery, it uses too many complicated or unusual words or phrases.

Collins says:

flowery (adj.): full of figurative and ornate expressions and fine words
(said of language, style, etc.)

One writing coach advises:

Avoid “flowery” language at all costs! If necessary, throw out
your Thesaurus! Readers are more impressed by the quality of your ideas than your use of multi-syllabic terms.

You can say that they are using big words. The idea behind the expression big words is that instead of using much simpler and more understandable to the average person words, some people intentionally choose to use words that sound more sophisticated, too intellectual or just clever. Oftentimes, the use of such words is unjustified. The main reason people do that is that they probably want to make themselves sound smarter than they really are. Here's how the Merriam-Webster Dictionary describes this expression:

a difficult word used to try to impress someone

And it also alongside the definition provides the following example sentence:

You don't need to use big words to make your point.

The word pedantic would fit, in the sense of an ostentatious display of knowledge.

Edit: Apparently this sense of pedantic is not very well known so to back the sense I mentioned:

• 
  pedantic, Merriam Webster (sense 2): "narrowly, stodgily, and often ostentatiously learned"


• 
  pedantry, Collins: "(British English) the habit or an instance of being a pedant, esp in the display of useless knowledge or minute observance of petty rules or details"


• 
  pedantic, Free dictionary (citing the American Heritage Dictionary of the English Language): "Characterized by a narrow, often ostentatious concern for academic knowledge and formal rules"

Such a choice is a matter of tone and style. I'm not sure that I would ever agree that it could be "not justified" as there is always at least a subtle difference in rhythm and flow, and often in meaning. Intentionally choosing or avoiding words with latinate roots, for instance, can be valid style choices. Intentionally choosing a less well-known term can affect style, possibly giving an academic air, or a more everyday feel to a piece of prose. Also, a word's history, via its etymology, can influence how it will affect knowledgeable readers.

So I might describe such a choice as "using a more intricate style" or "a more complex style". Style should suit purpose, of course. If the intended audience will not be likely to get a nuance, and may well misunderstand a word, that was a stylistically poor choice. If the intended effect will not be enhanced by a particular choice, that is also poor style.

sesquipedalian

To use long words, usually to sound clever, confuse someone or obfuscate a point.

The word bombastic seems to exactly describe what you're looking for, because it implies the use of complicated words. Cambridge's definition:-

using long and difficult words, usually to make people think you know more than you do:

To add a few more useful words:

• Grandiloquent: Pompous or extravagant in language, style, or manner, especially in a way that is intended to impress.




• Magniloquent: Using high-flown or bombastic language.

Definitons are from Oxford English. (These definitions also indicate pompous, extravagant, high-flown & bombastic as useful words.) I appreciate the irony that these words are themselves grandiloquent :)

Most of the answers above involve such uncommon words as to be self-referential. A more common idiom only mentioned in @Canadian_Yankee's comment would be any of [using a]

twenty-five cent word
five-dollar word
ten-dollar word

[There's been a bit of inflation over the years. My dialect still uses the middle one.]

They all have the same sense:

A long and uncommon word used in place of a shorter and simpler one with the intent to appear sophisticated

An answer has already been accepted, but I think a reasonable alternative that comes to mind is

jargon, which usually implies unnecessarily complex language, usually specific to a certain field.

Using the more complex word outside of that field is almost always unjustified.