Mindgames is a stupid name for it which will confuse new people and make them feel like they're missing an aspect of the game they can't understand. Just call it prediction. Thats something everyone can understand. If someone always follows a certain pattern of movement and attacks in a 2D fighter - eg spamming smashes - then do what punishes that predictability - eg, fast moves which work around Smashes, or a counter in the time frame they usually spam them smashes if you're Marth or something.
Prediction, reading enemies styles, thats what the community should present it as. Easier to understand, then. You don't need to do it generally until an enemy is owning you, but in a very uniform way that could benefit from being countered. If they can own you even after you render their current fighting style useless, well, then they're a better play than it looked like and you're gonna have to predict that too or else you'll get killed.
Theres nothing stating you can't play purely off your reaction times if you make sure everything you do is hard to counter and that your enemy isn't the type to predict your movements easy.
Thats why predicting is as important as combo knowledge and technical skill. When you predict someone, you want to punish them by seeing two steps ahead with a counter move before they predictably do what you, well, predicted, aye? Punishing works much better with technical skill as you can punish for higher damage, and thus win easier.
You can however over predict. Its when in simple games like Pokemon you're vs a fire type, have a water type out and expect them to switch to an electric type as its logical for them to; but they out thought you, and instead kept their fire type out even though you switched to a grass type to weaken electric moves. Pokemon takes up your turn to switch and you can't see what they're gonna switch to before they do it, so you have to predict, mhmm?
Smash and other fighters follow this mechanic of prediction but more loosely. If they're spamming shield grabbable moves vs you, shield grab them. If they're spamming them at you as they need to, but are variating between unshield grabbable moves to make it harder, then you're gonna whiff grabs at the air. If you over predict and wait for an unshield grabbable move, they can take advantage if they're smart or really oblivious to 'mindgames' and prediction by spamming you with shield grabbable moves when they need to.
Very loose example and theres probably more choices in that situation, but its an example.