What is the fallacy for the deliberate use of big words to confuse the audience?

This would be argument by gibberish I believe. 

Edit : actually I've been talked out of it above. Just using words other people don't know isn't a fallacy. 

Proof by Intimidation

Argument by Gibberish

As others have pointed out the closest paralogical fallacy would be an Appeal to Gibberish. However, from what you've presented in your question it is entirely subjective and open to interpretation, speculation, or an opinion whether the speaker intends to confuse the audience, gain credibility, or not.

In which case, there are too many variables to dismiss it as a fallacy when it could just as easily be a cognitive bias or blatant ignorance of the audience involved. 

Imagine a medical doctor or theoretical physicist lecturing before an audience of hairdressers. It would be perfectly acceptable for the speaker to use "big" words specific to the subject at the risk of not being understood, yet also innocent of the charge of doing so purposefully in order to confuse, or puff up his or her bona fides.

Word Salad fallacy. 

Perhaps the use of an expanded vocabulary was not INTENDED as a tactic, but simply commonplace to the user?  In which case, there would be NO fallacy at play.  I would need to see an example, in context, to make a fair determination.  It is also easy to find oneself out of their element or comfort zone when highly-specialized jargon is employed;  for example, I have been reviewing an unusual number of studies by virologists and other medical specialists of late, and the logisms they employ are very difficult for a layperson to assimilate.  Could you provide an example of the obtuse language you question?

I think you're looking for Proof by Verbosity/Fallacy of Intimidation. From what I understand the definition of the fallacy would include the deliberate use of complex or obscure wording to make a claim difficult to understand.

You do still have to be mindful of context since some people just habitually talk a certain way, ramble or don't know they need to explain the term. If you're willing to give them the benefit of the doubt about their intentions, pointing out the issue and asking them to explain themselves in a more accessible manner would be a good idea.