Most games are largely linear experiences. Rarely will you find a game that shoots off in a completely different direction according to the player's whim. That is because creating different branches to the main questline / narrative / progression / whatever you want to call it requires a lot of extra assets and programming. You're introducing redundancy, and no publisher or financier is going to like that. You're not gonna get the OK to create two different progressions of levels, for instance, to let the player make a real choice (go to the moon in a homemade rocket or visit the Buddhist temple?).
Some games feature different endings, like Bioshock or Baldur's Gate 2. However, these are usually just prerendered videos or cutscenes of some kind. They don't change the meat of the game.
Because of this fundamental linearity, the kind of choices the player can make is gonna be limited. You can wear different outfits, equip different weapons, visit different areas of the game world and so forth. That doesn't mean the game isn't largely linear, however. It starts somewhere and will end up somewhere else. Pure sandbox games are relatively rare. And even something like GTA doesn't allow any meaningful, world-changing choices to be made. You're limited to moving around that city, taking quests or climbing mountains that the developers put there for you.
Because of this, it is possible to largely predict what most players are going to do in the game and how its various stages will roughly develop (otherwise level design would be impossible).
Of course games have protagonists. Not all of them do, and the relation between the player and protagonist can vary, but it's a pretty common thing. Mario is obviously the protagonist of Super Mario World. Lara Croft is obviously the protagonist of Tomb Raider. Tetris, on the other hand, doesn't have a protagonist. It depends how much your game's mechanics are dressed up with characters and plot. Not every game needs to be a purely mechanical thing.