Game options allow players to tweak the game to their preference. With a wider audience of players these days especially on mobile, it’s even more important to give players more options. Game options are good because:

They can be turned off

If a player doesn’t like a game option that’s ok; they can turn it off so it won’t irritate them, be it turning off sound/music etc.

It can be a deal breaker for some if the option isn’t there

Players each have their own skill levels. If they get stuck and you don’t offer hints or a difficulty setting, some players will simply give up.

It can add more gameplay time

Different modes and difficulty, different characters etc can add more re-playability and add more variety to the game.

They feel like the game is theirs

When players tweak game options they can get sense of ownership as they’ve personalized the game to their preferences. This makes the game feel like it’s for them and so they’d might more likely play the game and more often. An example is some people might not like playing games they require them to tilt the phone because they think it’s silly and so if you give the option for non-tilting, they get a sense the game is made for people like them.

As for me

Eternal Pain has an easy/hard mode, on/off buttons for sound and music and an option to continue playing with your current score instead of reseting to zero when you die. It also has an unlockable high score mode and multiplayer mode.