I don't think these terms are very useful for a lot of stuff, and as far as tabletop adventuring and role playing games go most would fit into all these categories or none. I like where you are at with aggregation though!
At the core I think adventure games are strategy. But I did almost gave it it's own category myself when I made the list.
Strategy would be by far fullest and could use more subdivision.
Luck category would be needed for a few games.
Card/dice category could be removed (strategy/luck)
That would be something pretty dependent on play style which is unique from table to table. As far common language game terms are defined 'strategy' has a pretty clear meaning at the table and in computer games. Likewise, I can see some utility in calling D&D a dice game, but it is nothing like another dice game I love which is cee-lo.
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