What should I do if I encounter difficulties with launching the game from the account with the restricted rights?

You can try to add xpromo.g5.com in the list of unrestricted websites. 

Follow the instructions below:

• Go to System Preferences.
• Select Parental Controls.
• Sign in the username and password.
• Click on Website Restrictions.
• Select Allow access to only these websites.
• Add xpromo.g5.com to the list.
• Press OK and start the game once again.