To put the question on a factual (though still debatable) basis, I think we’d want to put the players in non-overlapping tiers. That is to say, if a Tier 1 player plays a Tier 2 player, the Tier 1 player will almost always win. If the Tier 2 player plays a Tier 3 player, the Tier 2 will almost always win, and so on. The question, then, would be which game has the greatest number of tiers.
A game of pure luck, like Chutes and Ladders, Candyland, or War, would then have only one tier: If you had a World Championship of Candyland, and then put the winner of that in a best-of-ten versus someone who had just picked up the game, they’d still most likely go five and five.
A simple solved game like Nim would have two tiers: Tier 1 would consist of everyone who knows the solution, while Tier 2 would consist of everyone else. There will still be some differences of skill among the Tier 2 players, but not enough that the best Tier 2 player would always beat the worst (thus creating a new tier).
For chess, we can look at Elo ratings. I’m not finding exact numbers for 95%, but (if I’m reading the tables right) it looks like a player 366 points above his opponent should win about 90% of the time, while a player 677 points above should win about 99% of the time. Let’s eyeball that as a difference of about 450 points being the 95% cutoff. The lowest ratings are either 0 or 100, depending on governing organization, and the highest are about 2900 for humans, or an estimated ~3300 for computers. That would give chess 7 or 8 tiers.
I’m not sure where to start for estimates for other games.