So it means, even if I can download the game (there is a download button), this does not give me the right to use this game for any of my purposes (commercial, for example, and distribute)

In the majority of cases, downloading a game gives you only the right to play it. Re-distributing it is a major no, with very few exceptions. If a game has no license, by default in most countries, you are not allowed to publish it in any way.

Please respect the time people put on their creation and don’t try to profit from other people’s work.