Blockchain games are any games that include blockchain technology in its backend or mechanics in general.
The most often use for blockchain tech in games so far has been been to store your items on the blockchain, tying them to your (Ethereum) wallet and making them permanently your own.
In contrast to this, in “classic” games, any items that you supposedly own in-game are in fact stored on the game publisher’s servers, as is your whole account. There are many ways for you to lose possession of your assets in this case - server mailfunction (failure or attack), stopped game development, banned account, etc.
The first generation of blockchain games was solely based on this principle and they were focused on collecting unique assets and trading them, for fun, profit, or both. CryptoKitties was the game that started this trend and they’re still quite popular. Nowadays, we see games where blockchain technology is used to store assets and confirm and store player’s progress, but with an additional, more complex gameplay built around that.
Blockchain Gaming: Separating Signal from the Noise (blog post)