This is not correct. The article is needed.
On the other hand, if it were 'puzzles' (plural) the article would be incorrect (unless it were a reference to specific puzzles already mentioned).
Crossword puzzles are considered an educational tool.
(Correct is either 'regarded as an educational tool' or 'considered an educational tool'.)
The difference between "Kudos is a game for..." and "Kudos is the game for..." is that the first one is a simple statement of fact but the second is more emphatic as to me it implies "Kudos is precisely the kind of game people who love life simulation games would like to play".
No. "Kudos is the game for people who . . . " means it's the one and only game for such people, likely to be said only by those who are selling it. "Noughts and Crosses is the game you can play anywhere", similarly, says it's the only such game.
Unless you intend to make such a claim, the correct phrase is not "the game" but "a game".