What happens if my Daxos of Meletis deals combat damage to a player, and the card revealed by that player is a land? Am I able to play that land or does nothing happen, because Daxos's ability is worded as "you may cast" that card and you don't cast lands.
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The land is exiled and you gain 0 life. You may not play the land, because as you point out, the card says "cast" not "play":
The CR define what you can do in MtG, since no rule exists for Casting a Land, you cannot do it. Additionally, rules exist for cards that share the land type and an indication that lands are not spells (about the closest you will get that lands aren't spells).
You cannot play the land, because Daxos only allows you to "cast" the card. The land will still be exiled; and it will simply stay in exile.
You can see in 601.2, "casting" specifically means to put it on the stack, which you do not do when playing a land.
Also note cards like Djinn of Wishes, which allow you to play a revealed card, as opposed to allowing you to cast a revealed card. That's the wording needed to allow you to play a land.
The land will be permanently exiled. Specifically,
If Daxos of Meletis instructed you to play the card, that would be a different story. To play card is either to play it as a land or to cast it as a spell. You would be able to put the card on the battlefield for free if it's your turn and if you haven't already played a land that turn. It would count towards your limit of one land per turn.
If Daxos of Meletis instructed you to put the card on the battlefield, that would be a different story too. The card would immediately be moved directly from your hand to the battlefield. This wouldn't count towards your limit of one land per turn.
Interestingly, there's no rule forbidding casting a land. MTG will simply never let you do it.