There are many axis in games. Symmetric <-> Asymmetric Hidden information <-> All information public. Cooperative <-> Full Competitive Fiddly / Tons of Rules <-> Simple Abstract <-> Deeply Thematic Stochastic <-> Deterministic Interaction <-> Disassociated And several more. I personally like asymmetric, some hidden information, possibly a traitor, competitive, fiddly, thematic, a little stochasticity, and interactive. And, hence I feel that Dune by Avalon Hill is the best game ever. In general the discussion between Euro and Ameri games is two large potential clusters of styles liked by gamers.
That's a great list.
My choices
Asymmetric - Love Imperial Assault/Descent II
Public - Like chess the idea is misdirection and traps. Even if you have perfect knowledge you don't know your opponent's mind.
Voluntarily Cooperative - Work together when it works, but co-ops are getting boring.
Simplistic - Not something simple, but mechanics that always work the same, no surprises.
DEEPLY THEMATIC - The more theme the better. I would love Waterdeep if it was meeples instead of cubes.
Deterministic lite - I think that every game needs random elements, but I hate snakes and ladders.
Interaction - Play the other players, play against, play with, overcome the environment. Great list!