Depends on the genre to me. Action games are my favorite genre, but it is also probably the most linear genre as well. Exploration is quite limited, and the games pretty much push you down one path. However, getting from point A to point B isn't really where the value lies in actions games. The value lies in the gameplay mechanics, combat depth, and overall fluidity. Point being, while the game is linear in structure, the gameplay allows you to approach battles in different ways, utilizing different strategies, different weapons, etc, and that is what gives action games replayability.
I feel that stretching the term linear to encompass gameplay mechanics is reaching too far (don't know if this is what the OP means when he talks about doing the exact same thing on multiple playthroughs). The real problem I see with this argument is that almost all games would then become non-linear because you can almost always use different strategies when playing a game, whether it be an action, shooter, rpg, etc.
I guess my main point is just that linearity is more acceptable in some genres. For example, I prefer my action games to be linear while I am less forgiving when it comes to RPGs that are linear.
