I believe that a lot of people get sidetracked on the argument of whether mindgames exist or not, because the term is misused and abused so often. Sometimes it is misused jokingly (when my friend Phantasms off the stage, I can't help but shout "Mindgames!"), and other times it is simply ignorance. Not ignorance meaning stupidity, but ignorance meaning a lack of knowledge on the subject. Also, some people label "tricky" or "smart" gameplay as mindgames. I don't completely believe that's true, but it's just an example of the many ways that people define mindgames.
I do believe that it is difficult to determine whether mindgames exist or not because to me, mindgames is a concept. It is an intangible, not a concrete visible strategy like wavedashing or L-Canceling. It is a combination of many things including strategy, predictability, trickery, and analyzing. It is very broad because of this conceptual property.
Since mindgames is conceptual, and mostly within the mind, nobody can completely state whether mindgames exist or not. "Mindgames do/don't exist" is a statement of opinion, not fact, unless the Smash community has an exact definition of mindgames. If mindgames does indeed have a true definition, then one can truthfully state that mindgames do or don't exist.
The question "Do mindgames exist?" is very debatable, but it is safe to say that the idea of mindgames, or the concept of mindgames, exists.