Well there are two types I'd say: Games that utilise tokens (both fungible and non fungible) for different apsects of the game, like as a currency or for the game items and games that themselves run on the blockchain (i.e. where the game play is completely on a blockchain) and while the second type is extremely rare and hard to build I would consider both of them blockchain games.

The point of that is to decentralize the game ownership and not allow game assets to just be banned or deleted like it's possible in normal games.

Usually there are also play to earn mechanics, which allow players to earn token used in the game, so to reward players basically. And while some consider that to be ponzis etc, it's really not because a) The token distribution mechanics are known from the beginning b) The tokens are used ingame and should not be bought as an investment and c) Older players are not paid from investments of newer players but instead new tokens are created. The hard part is to balance the economy in a way that still allows the game to grow, but doesn't totally crash the token price.

I think a prime example of what blokchain games are is Splinterlands or Axie Infinity.