So when someone downloads my game they receive the game to play on their computer? Can I have it so they can just play the game without giving them the game?
There is no streaming play service on itch.
Either you make a web game without download option or you make your download options cost money. Then you can have demo versions for free. And if you have pay what you want option, downloads that paid 0 will not be able to "claim" your game, should you increase the price later.