Does this game has an actual end ? I have just defeated Alduin for the second time and I have run out of quests to do ? So what am I supposed to do to finish the game ? Or is it a game that really can't be finished ?

Why would you ever want an Elder Scrolls game to end? That is the beauty of the series.

The game ends when you stop playing.

It ends when you're not having fun anymore. The more creative and clever you are, the more fun you can have, the longer the game lasts.

The game doesn't end when you've finished the main questline or any/all of the other questlines in the game, that's what makes it so fun. The dungeons reset after certain amounts of time and there are radiant quests to keep your character busy

I'll say what I've been saying for years: "You don't 'beat' an Elder Scrolls game. You live it."

That's very well said. An Elder Scrolls game doesn't end until you delete the character or just outright quit it. The main quest can be finished, but it won't end the game for you.