As there are many reasons why you need an Game Classification system. Basic thing when setting some new Classification System is to check out the Dimensions that should not overlap. For example for an pain classification System you could have the dimensions location, strength and also type. One attempt you can find in wikipedia https://en.wikipedia.org/wiki/Game_classification#cite_note-CAATM-4 is the question who get killed. Which is an really specific question. So one dimension maybe violence occurrence. Than start by a far look it would be Yes or No. Only No needs nearer specification. But that category maybe only an sub category of the Content Dimension.
So far here is what i have.
GAMEPLAY
→Skill addressed
→Luck Skill ratio
→Interaction methods
→Used Models
APPEARENCE
→Visual
→→View type
→→Style
→Acustic (ignored by most)
OTHER CONTENT
→Violence
→Story flow type

Agreed, that's a very good way to start. What would be the dimensions relevant for the classification of video games?

The List is still in work:
GAMEPLAY
→Skill addressed
→Luck Skill ratio
→Interaction methods
→Used Models
APPEARENCE
→Visual
→→View type
→→Style
→Acustic (ignored by most)
OTHER CONTENT
→Violence
→Story flow type
→Grade of Realism