It appears that both the ‘Block literal IP addresses’ and ‘Block VPN,Tor, and Proxies’ options prevent the device from accessing Hearthstone games (they can load the client just fine, but when it goes to join a game it times out). I tried each option enabled individually, but hearthstone would not work without both of them disabled. Is there a way to re-enable those features and grant access to Hearthstone?
In general, you need to disable both restrictions to play games with installed game client. However, if the game uses a limited number of root domains or IP addresses, you can try to white list those domains/IP addresses with the restrictions enabled.
To find out what is blocked for what reason, you can enable the restrictions, try to play the game, and then look at the parental control logs for blocked requests in raw format.