Best answer by SophiaC
I agree, these permissions concern me. Some of them can definitely be used for malicious purposes, like drawing over the screen, reading your contacts and deleting files from the SD card. For some of these permissions, I can't imagine why a game controller app would need them, for example phone and calendar access. I looked around at some similar apps and none asked for these permissions, though at least one requires rooting the device!
With a little research around the web, I'm guessing you're downloading this app from a website, not Google Play. Whenever you download apps through a source other than Google Play, use extra caution.
That being said, I didn't see any clear evidence of this app being malicious, but the information I'm getting may not be for the specific package you're installing since I don't know the file hash.
If it were me, I probably wouldn't install this app. If I really wanted to use the controller and there wasn't a good alternative, I would do more research with the specific apk's file hash. Without that, this is the best information I can give you.