Poker is a game of skill just like backgammon. You can wager money and there is risk (chance) involved, but you can develop skills which will ensure that you are a winner over a less skilled opponent. Just like golf. There is always the chance that you will not make the necessary strikes and a less skilled opponent takes a game from you, but over the long run, you can sufficiently influence the outcome and achieve a positive win rate. This is what makes it a skill-based game. You influence it by your skills. You can place wagers and gamble on the outcome, but that doesn't suddenly make it any less not a game of skill.
I'm not very familiar with fantasy sports, but to the best of my knowledge, the same holds true there too.
A game of chance cannot be distinguished from games of skill. All games involve chance. This problem probably arises from the poor understanding of "chance" and probabilities by the people who wrote the law (presuming Hanlon's razor here). They wanted to ban games where the operator bleeds the players dry, like slots, lottery, etc., and called them "game of chance", but there is more to the story of "chance", like i outlined above.
The definitions are different in each case, but none of them work that way. In New York, for instance, the outcome depending materially on chance, whether or not skill is also involved, makes it a game of chance.
Given the government's heavy use of lotteries and other gambling as a cash source, the laws appear to be designed by lawmakers with a solid understanding of chance and probability and a desire to ensure that monetary gambling (with gambling defined as "an activity where the influence of chance outweighs the benefits of skill, for most participants") be restricted to the state, not commercial entities.
The relevant point being that not everybody believes they're a "game of skill" in the "skill vs. chance" slider which is relevant to the law. While there's no question that like every game, user actions (skill) can impact the outcome, how much it can impact the outcome is what determines whether something is classified as a game of skill or chance. Perhaps it's more clear if we say "a game of primarily skill" or "primarily chance".
If daily fantasy sports is primarily skill-based, they can do it. If it's primarily chance-based, it's illegal in the US. Which is why they're pushing for it to be referred to as "skill-based".
Very few games that we'd call gambling (e.g. blackjack) are 100% chance though. Maybe dice games? Lotteries? Even in games where the house always has edge, you can lose less by playing optimally.
Losing less does not mean you can win, which is the case in poker. To the best of my knowledge, it is the case in fantasy sports too.
Roulette and slot machines.
Honestly though I reckon it's a fine line between a person day trading their pension, a spread better and a poker player.
At the very least I'd love to see how it's distinguished legally.