Over my stay on the Internet, I have seen many self-professed "true gamers" going on about how gameplay is the most important thing in a game, to the detriment of everything else, with graphics being a common victim. They enjoy feeling superior to the other sheeple who judge games solely based on their photorealistic graphics or lack thereof. They almost worship this gameplay thing as if it is indeed a deity, putting down those that worship a false god. A minority among them even goes so far as to almost imply gameplay and graphical qualities are mutually exclusive, becoming instantly suspicious of any game that has good looking screenshots.
However, for this supposed holy grail of game design, gameplay is a vague term. Ask ten people what they think gameplay is, and you'll get ten different definitions. (That is, if they are all capable of even giving a definition. For many, gameplay is one of those things you just have an innate ability to recognize, but can't be described in words.)
To progress, we must make an attempt at defining gameplay, then. Gameplay is something exclusive to games, something other forms of entertainment, like films and books lack. Gameplay must therefore be related to the interactive elements of the game. I choose to define gameplay as the set of all mechanics present in a game.
Those mechanics are the way the game interprets your input. If seen as a state machine, the mechanics are the state-transition function of the game. They determine what happens when you give a certain input while the game is in a certain state.
A game is a system that takes input from the player, processes it, changing its state, and feeds output to the player. The player recieves that input, and based on it, decides what input to give the game.
The output is given through light and sound. Since we mostly use our vision to map our surroundings, we get most of the data from the first source.
Good graphics should convey the information to the player in an effective way. If they don't, the connection between the player and the game is broken. If we take the metaphor of the mechanics being the plot of a book and the graphics the font, not having well thought out visual content is like having the book written in Zalgo.
You need good UI design to tell the player all the information needed to play the game. You need to allow the player to be able to tell interactable objects from those that are simply background. This is why graphic design is one of the most crucial parts of a game. If the player can't tell what's going on in the game world, you have failed as a game designer.
Even when it comes to the purely aesthetical elements, polygon count and resolution are far from the most important elements. You may have the best graphic processing technology avaliable in the market, but that won't save you if the visual style is not well thought out. If your game looks like the visaul equivalent of the Crazy Bus theme, even if your mechanics are the best in the world, no one will want to play it.
Your visual style has to be coherent and fit the game's theme. A dull brown and grey color scheme will simply not work on a game about cute cartoony animals, the same way as vibrant, high saturation colors will not work in a realistic war shooter. Avery visual element has to fit with the rest, or the players will notice how out of place it is. (I know that something that obviously doesn't belong with the rest can be used to create a sense of creepyness and mystery, but unless you really know what you're doing, you should stay away from taking these kinds of risks.)
A good style will do a lot for your game's appeal, and you don't need to have the best of what's around to be able to create that style. Even a pseudo 8-bit look can be extremely appealing if well thought out.
In the end, the visual elements are one of the most important parts of game design. They help the player know how your game works and set the mood. Even if you see yourself as a pure coder, if you have an interest in game development, learning some principles of graphic design will do wonders for the quality of your work.
And that about wraps it up. I'll end this with a question for my readers. How do you define gameplay?