Unfortunately, I lack the ability to properly communicate the experience of playing Magic as opposed to other games. I can point to a few aspects of the game, though:

1) It's not static. Magic changes all the time because new cards are released every few months. Chess and Go have been Chess and Go for hundreds of years, and they've been studied to death. Relative to other classic games, Magic is a game that gives more rewards to experimentation and discovery.

2) There are random factors in Magic. This adds excitement; to paraphrase a saying about American football, on any given day, any player can win. The best player at your local tennis, Chess, or Go club will never, ever win a match against the current World Champion. In Magic, although the better player usually wins, upsets can and do happen. This can even be fun for the better player, who can still have the experience of trying to claw his or her way back from behind, even against lesser players. (On a related note, some games are harder to handicap than others; Go has an elaborate system in which weaker players are given handicap stones at the start of a match, but handicapping Chess players is more difficult. Magic handicapping is trivial; just change the decks each player is using.)

3) I find trying to think zillions of moves in a chess or chess-like game difficult and stressful. Magic doesn't present players the task of dealing with ridiculous game trees but still manages to continuously present interesting decistions to make, thanks to random factors and hidden information in addition to a moderate amount of visible complexity. It's more about who has better quality heuristics than brute-force look-ahead.

4) Competitive Magic has a large infrastructure and community devoted to it. You can find small tournaments all over the world, and Magic Online is almost always available. There are also larger, more prestigious tournaments, too, many of which have significant cash prizes and some of which are invitation-only, up to and including a World Championship. If you have cards and want to play Magic competitively, it's easier to find opportunities than it is for many other games and sports.

5) It almost goes without saying, but playing Magic is fun and exciting. They don't call it "Cardboard Crack" for nothing.