I would suggest going with **a bar loading screen** which basically informs the user that content is loading and you are preparing them for an unique experience. You can also try to engage the user by informing them about the game and the experience offered

 For example Empire total war informs the user about what he can experience in the game

![enter image description here][1]


This game Nyrthos gives historical information about the game background

![enter image description here][2] 

This loading screen provides information about the characters the user can play in the game

![enter image description here][3]

This screen provides tips on how to be successful in the game

![enter image description here][4]

I **strongly recommend against providing an alternate game in the loading screen** as you are distracting the user from the focus of the game and are not utilizing the time he spends waiting in enhancing his experience and enthusiasm about the game (as the above examples have done). Also apparently [Namco Bandai holds the patent to have minigames on their loading screens][5] only so unless you work for them, you are opening yourself to [legal issues][6].


**Edit :** Based upon your update, since this is a simple game, I would still recommend a simple bar screen but provide information about how the user can play the game (like shortcuts or codes and so on). For example taking this web cricket game, in the loading screen it just basically shows me the controls

![enter image description here][7]

You can also use the screen to provide tips as shown below

![enter image description here][8]


  [1]: https://i.stack.imgur.com/DBVFt.jpg
  [2]: https://i.stack.imgur.com/rs4rl.jpg
  [3]: https://i.stack.imgur.com/F4OdL.jpg
  [4]: https://i.stack.imgur.com/h21QC.jpg
  [5]: http://www.pixlbit.com/news/213/namco_bandai_owns_loading_screen_minigame_copyright
  [6]: http://www.sticktwiddlers.com/2012/08/09/why-namco-games-are-the-only-titles-with-mini-game-loading-screens/
  [7]: https://i.stack.imgur.com/WitoU.jpg
  [8]: https://i.stack.imgur.com/tVZ4O.jpg