Can you download with no problem the app Stickman and not damage your Raspberry Pi (a Raspberry Pi 3 in particular)?
Another question I have is if you can play League of Legends, Hearthstone, etc.
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The quick answer:
No, you cannot run it on the Pi at this time (same goes for the other games you mentioned).
The full answer:
Stickman is a Windows GUI application. It requires the full Windows OS to run properly. Unfortunately, as of this time (Dec 2017) there is not a full version of Windows that runs on the Pi, or any other ARM-processor device. There is a lightweight IoT version of Windows that runs on the Pi, but it is not intended for running full-fledged traditional Windows applications and/or games.
If either of the following is true then yes, otherwise no.