This is a tricky question.
The publisher of that game is a large and well established games developer. In general, such companies can be trusted to not do funky things. If the game was made by a small unknown company you'd still likely be fine, since MS tests every app before uploading it to the store, but MS isn't perfect either. At the very least the risk at contracting malware is still very low. So far there is no known malware on WP.
The game itself doesn't actually require any of the listed permissions. Those are required for the advertising and data collection software that is integrated into the game. Free games are nothing but legally sanctioned spyware. Spying on you is legal, because you agree to let the app record and report private information about you, in exchange for getting the game without paying for it. Most people care more about saving a dollar than they care about their privacy.
I have no problem spending money on software, I despise advertising, and I value privacy, so I would never install an app that requires such permissions on my phone, but that is your own decision to make.
In this specific case, you certainly don't have to worry about the game screwing up your phone.