A game is composed of a whole bunch of things and because I have no desire (at the moment) to discover if anyone else has coined a term for these things, I will call them elements. Everything from graphics to animations to sound effects to possible outcomes from pressing a button… each of these things is an element. You can also grasp larger concepts and call them ‘elements’ as well; the definition is not a clean one and for these purposes they aren’t meant to be.
I was going to write something big, with examples, but maybe I’ll keep it simple this time.
When one designs a game (without creating it), a number of its elements are explicitly defined. Many, however, are not defined because they come about as a result of combined elements. Thus, as a game is created, harmonic elements will join together to add new and fantastic elements, only some of which could have been considered beforehand. Some examples of these are unique tactics that only a few think to use, and evoked feeling as a result of any combination of elements (minor-scale music with long notes, sparse level design, and certain character design or animation could come together to evoke a feeling of loneliness much better than any of those elements alone).
Consider a NULL GAME that contains no elements.
To this game, you add a sound effect that plays endlessly, a button that does nothing, and a player sprite that animates randomly. You do not have a game, and there is no elemental harmony.
To another null game, you add a jump sound effect, a player sprite with a jump animation (and a land animation), and a button that causes you to jump. There is no game here, but there is already coherence, harmony, between the elements.
At this basic level, it is obvious that elemental harmony is important.
There is a little more that I have to say. Consider, now, a Metroidvania (bit of a jump, I know!) with no powerups to speak of… yet. To this game you can add three powerups that effectively act as keys to doors; you have a literal gold key which you can use to attack only a few gold doors to open them, a flute that can be played to make a certain type of waterfall dry up, and a set of armour that gives you a little more damage resistance — and also protects you from spikes on the ground. Here we have elemental harmony, right? The key + door harmony is obvious! Flute + waterfall! Armour + damage + spikes (triple harmony!).
I hope you didn’t take me seriously, because in a game such as a metroidvania there are (usually) so many other elements that exist with which to interact!
Armour is a passive item, meaning while it can protect you from spikes and make you a little more durable, it will never introduce new tactics: it will pretty much just make every tactic a little bit easier (except against tougher enemies). I claim that passive abilities have awful Elemental Harmony.
The Key and Flute, while active, interact with (as described) a single type of object in a predictable way. Doors vanish. Waterfalls vanish (and at best might lower water levels to change levels in an unexpected way). Key-type items have terrible Elemental Harmony too.
Instead of one of these three items, one could grant the player a Freeze ability that turns water solid — a waterfall’s source could be blocked, water surfaces traversed, and water enemies could be blocked or trapped. In this way, it interacts with the environment instead of simply removing part of the environment, and level design (game design too!) can revolve around the resulting complex elements (solidifying the wrong water can block you off! freezing waterfalls below the source may work with even simple water physics to redirect the waterfall!) instead of the boring and unimaginative ‘simple element’ of removing doors or waterfalls.
I will conclude with a disclaimer: Elemental Harmony is just another bullshit term coined to describe some part of what makes games magical to some idiot game designer in this soup of ‘indie games’. My hope is that this article will cause someone to create a ‘better’ game due to designing it with more Elemental Harmony in mind, and, perhaps, become a ‘better’ game designer.