I have a Kindle Paperwhite 4 and I just wonder, besides reading books, are there any games to play on it?
Of course a Super Mario might be too demanding to the display. However, I suppose a crosswords or Sudoku should be technically feasible?
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Games (and Apps) for Amazon Kindle Paperwhite are known as an Active Content and you can search Amazon Store for them here. Some of these games are for money, some are free.
However as stated here they are fully supported on Paperwhite 1 & 2 and partly version 3, version 4 is not discussed at all. You have to test each and one you wish to try. Please leave a comment to complete my question on this topic.
Regarding controls, I found an article describing basic kindle paperwhite game controls here. This can help you, if there are any games working on your device.