A game genre refers to the type of game. There are several game genres to date.
Action games are made with physical challenges that require good hand-eye coordination and high reaction speed. Action games may also include other challenges, such as racing or collecting objects, for example, although they are not really central to the genre. They usually place the player under time pressure. A good number of action fangames can be found on MFGG.
Arcade games are, perhaps, the most general game genre. Instead of being classified by its game mechanics or level design, arcade games are based around trying to score as many "points" as possible, usually under a time limit or scaling difficulty curve. Many minigames are the arcade genre, as this genre is generally agreed to be the easiest to produce, and fits well in a smaller-game environment. An important distinction should be made between arcade games, and games with arcade elements (such as Super Mario Bros.) Simply having a points system does not make a game an arcade game, it must be focused primarily around achieving these points.
It is very common for arcade games to have a "high-score" chart, as it is an obvious and age-old feature. In addition to that, Game Maker has a built-in high-score system, thus making it's implementation take minimal effort.
The name itself originates from games in an "arcade", where the goal of most games were to prove your skill by achieving a spot on the high-score chart, as every body who plays the game afterwards would see your name and score. Their game was also economically designed to defeat the player rather quickly (as previously stated, either with a time limit or harsh difficulty curve), as that would allow more players to play in faster rotations, or frustrate the player into playing again. This is known as, "eating quarters".
Fighting games usually have two fighters face each other and use different attacks on their opponent by pressing different keys. Fighting games tend to have different playable characters, where they have different attacks, strengths, and weaknesses. Fighting Mario fangames aren't very common, but they do exist.
Minigames are small games that can have any type of gameplay, most of them would have a high-scores table. Some games are known as Minigame Compilations, where they have more than one minigame. Minigames are quite common in MFGG, due to their small size. They even have their own competitions. Most minigames are also arcade games, as that genre is well suited to being small in size. They are not, however, inherently small and many of them are quite large.
A platformer (or platform) is a game genre in which the player's character goes across "platforms" to get to the end of the area. Typical platforming games involve the character moving left and right, and jumping to overcome platform heights and obstacles. Platformers are very popular, and in fact, make up the majority of the fangames on MFGG.
A puzzle game requires the player to manipulate one thing, which in turn allows you to complete a task. There are not very many puzzle fangames, and most of the existing ones are considered to be of poor quality.
Role Playing Game
A role playing game (or RPG) is a game in which you gain some form of experience which increases some stat relevant to the player. It has been argued that an RPG requires a specific sort of combat system, however a great many RPGs designed more innovative combat systems. While there are a fair amount of RPG fangames, they are not popular to make because they require much more for-thought and time to produce than most other genres.