Two Apple Developer Accounts
As long as you have two different Apple IDs, I don't think there should be anything against registering for example two personally owned businesses (or sole proprietorships) with seperate developer accounts - even though both are owned by the same person. It might depend on the legal situation in your country/state.

The best way to find out is to contact Apple and ask them if they see any problems with having two accounts.

However I must note that there is no problem in releasing multiple apps on the same developer account. You can mix games and business apps in the same account without any problems.