This article will provide an overview and random methodology for designing an arcade game.
I'm just regurgitating what I think I've learned, so don't take it too seriously.

Arcade games were a commercial avenue for electronic designers back in the 1980s. Basically, they made money.
They did this by requiring coins to be put into an arcade unit which enabled the player to play for 2-5 minutes.
2-5 minutes is good for business because more coins are required and no-one waits around too long for a turn.
In this arrangement, games with high replay value and popularity make the most money.

Therefore:
1) A good traditional arcade game can be played many times and still be interesting.
2) A good traditional arcade seems fair in terms of payment and play duration.
3) A good traditional arcade game is popular.

Being heavily cryptic, I cannot provide advice for point 3.
Being the modern gaming industry, point 2 is not valid unless you're literally making an arcade game.
Leaving us with point 1. Hmmm

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Remember you only want to keep the player for 5 minutes.
From this we know 1 rule about arcade games.
* Time limits
Genres such as turn based fighting are out. Without saves, you cannot level up characters. Without unlimited time, you cannot learn complex puzzles.
Every game element must connect to the capabilities of the player.
The game must provide avenues to exercise these capabilities.

These avenues are:
keyboard / mouse
computer screen

What will you bind to the keyboard or mouse? A picture!
What will you bind to the screen? The player!
What is a picture? Representative of something real, or a symbol denoting its function within your game.
Write a list of real stuff, Write a list of functions,
What is a player? Someone who can read, write, react and respond.
Write a list of situations, Write a list of reactions,

Select elements from the lists which work well together. Include these in your game and try to assign a skill number to each reaction.
When you code your game content, linearize player exposure to skill total variants (Levels).

Embellish the game with unnecessary graphics, sounds, text, and you have a masterpiece!

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Good luck on your creation!