We work with a partner company (Skillz Inc) to run all the account services and tournament operations in our games, and their system is what requires all of the permissions. From what we've been told:
The photos access is required so that you can provide a custom profile picture for their system
The contacts access is required because the game includes a "share your game" feature which lets you send out links a game where you won to your friends.
They also require location services to validate that you are playing from a place where the cash prizes are legal.
The way their system is integrated with our game is why it needs to request access at startup. I can definitely verify that the game and the tournament system will never make calls on your behalf or snoop on your pictures/videos in any untoward fashion.
If you want any more details on why their system requires these permissions (as they are used a number of other games beyond ours), then you can send an email to support@skillz.com and they should be able to explain everything in a little more detail.